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Deck 2: Functions and Graphs
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Question
Assuming that the graph shown has y-axis symmetry, sketch the complete graph. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Question
Given 
, use the algebraic tests to determine symmetry with respect to both axes and the origin.
A) y-axis symmetry only
B) x-axis symmetry only
C) origin symmetry only
D) x-axis, y-axis, and origin symmetry
E) no symmetry
, use the algebraic tests to determine symmetry with respect to both axes and the origin.A) y-axis symmetry only
B) x-axis symmetry only
C) origin symmetry only
D) x-axis, y-axis, and origin symmetry
E) no symmetry
Question
Estimate the slope of the line. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Given 
, use the algebraic tests to determine symmetry with respect to both axes and the origin.
A) y-axis symmetry only
B) x-axis symmetry only
C) origin symmetry only
D) x-axis, y-axis, and origin symmetry
E) no symmetry
, use the algebraic tests to determine symmetry with respect to both axes and the origin.A) y-axis symmetry only
B) x-axis symmetry only
C) origin symmetry only
D) x-axis, y-axis, and origin symmetry
E) no symmetry
Question
Question
Find the x- and y-intercepts of the graph of the equation below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Plot the points below whose coordinates are given on a Cartesian coordinate system. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find an equation of a circle that satisfies the following condition.Write your answer in standard form. Center: 
; passing through 
A)
B)
C)
D)
E)
; passing through A)
B)
C)
D)
E)
Question
Graph the following equation by plotting points that satisfy the equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Sketch the graph of the equation below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
The population 
(in millions of people) of North America from 1980 to 2050 can be modeled by 
where 
represents the year, with 
corresponding to 2050.Find the y-intercept of the graph of the model.What does it represent in the given situation?
A)
It represents the population (in millions of people) of North America in 2050.
B)
It represents the population (in millions of people) of North America in 1990.
C)
It represents the population (in millions of people) of North America in 2030.
D)
It represents the population (in millions of people) of North America in 2020.
E)
It represents the population (in millions of people) of North America in 1980.
(in millions of people) of North America from 1980 to 2050 can be modeled by where represents the year, with corresponding to 2050.Find the y-intercept of the graph of the model.What does it represent in the given situation?A)
It represents the population (in millions of people) of North America in 2050.B)
It represents the population (in millions of people) of North America in 1990.C)
It represents the population (in millions of people) of North America in 2030.D)
It represents the population (in millions of people) of North America in 2020.E)
It represents the population (in millions of people) of North America in 1980. Question
Find the x- and y-intercepts of the graph of the following equation. 
A) x-int:
; y-int: 
B) x-int:
; y-int: 
C) x-int:
; y-int: 
D) x-int:
; y-int: 
E) x-int:
; y-int: 
A) x-int:
; y-int: B) x-int:
; y-int: C) x-int:
; y-int: D) x-int:
; y-int: E) x-int:
; y-int: Question
Write the standard form of the equation of the circle whose diameter has endpoints of 
and 
A)
B)
C)
D)
E)
and A)
B)
C)
D)
E)
Question
Find the slope of the line that passes through the points 
and 
A) 9
B) -5
C) 5
D) 0
E) undefined
and A) 9
B) -5
C) 5
D) 0
E) undefined
Question
Find 
such that the distance between the point 
and 
is 10.
A)
B)
C)
D)
E)
such that the distance between the point and is 10.A)
B)
C)
D)
E)
Question
After completing the table, use the resulting solution points to sketch the graph of the equation 
Question
Plot the points and find the slope of the line passing through the pair of points. (2, -4), (4, -1) 
A) slope:
B) slope:
C) slope:
D) slope:
E) slope:
A) slope:
B) slope:
C) slope:
D) slope:
E) slope:
Question
Sketch the graph of the equation below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Match the equation below with its graph. 
Graph I : 
Graph IV : 
Graph II : 
Graph V : 
Graph III : 
A) Graph IV
B) Graph III
C) Graph V
D) Graph II
E) Graph I
Graph I : Graph IV : Graph II : Graph V : Graph III : A) Graph IV
B) Graph III
C) Graph V
D) Graph II
E) Graph I
Question
Question
The table below shows the velocities, in feet per second, of a ball that is thrown horizontally from the top of a 50 foot building and the distances, in feet, that it lands from the base of the building.Compute the linear regression equation for these data. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the slope of the line that passes through the points 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use the point on the line and the slope of the line to determine whether any of the three additional points lies on the line. Point
Slope
I: 
II: 
III: 
A) Only point I lies on the line.
B) None of the points lies on the line.
C) Only point III lies on the line.
D) Only points I and II lie on the line.
E) Only points I and III lie on the line.
Slope
I: II: III: A) Only point I lies on the line.
B) None of the points lies on the line.
C) Only point III lies on the line.
D) Only points I and II lie on the line.
E) Only points I and III lie on the line.
Question
Determine if lines 
and 
are parallel, perpendicular, or neither. 
A) parallel
B) neither
C) perpendicular
and are parallel, perpendicular, or neither. A) parallel
B) neither
C) perpendicular
Question
Question
Question
Question
Find the slope and y-intercept of the equation of the line. 
A) slope:
; y-intercept: 4
B) slope:
; y-intercept: -6
C) slope: -6; y-intercept: 4
D) slope: 4; y-intercept: -6
E) slope: -6; y-intercept: -4
A) slope:
; y-intercept: 4B) slope:
; y-intercept: -6C) slope: -6; y-intercept: 4
D) slope: 4; y-intercept: -6
E) slope: -6; y-intercept: -4
Question
Plot the points and find the slope of the line passing through the pair of points. (3, -2), (-4, -2) 
A) slope: 0
B) slope: 1
C) slope: -7
D) slope:
E) slope: undefined
A) slope: 0
B) slope: 1
C) slope: -7
D) slope:
E) slope: undefined
Question
Which of the following graphs below can be approximated by a linear model? I 
II 
III 
A) None can be modeled linearly.
B) Only graphs II and III can be modeled linearly.
C) Only graph III can be modeled linearly.
D) Only graphs I and II can be modeled linearly.
E) Only graph I can be modeled linearly.
II III A) None can be modeled linearly.
B) Only graphs II and III can be modeled linearly.
C) Only graph III can be modeled linearly.
D) Only graphs I and II can be modeled linearly.
E) Only graph I can be modeled linearly.
Question
Write the equation that expresses the relationship between the variables described below, then use the given data to solve for the variation of constant. "t varies directly as 
, and 
when 
"
A)
; 
B)
; 
C)
; 
D)
; 
E)
; 
, and when "A)
; B)
; C)
; D)
; E)
; Question
Suppose the average remaining lifetime for women in a given country is given in the following table. 
Compute the linear regression equation for these data, where x is the age, in years, and A is the remaining lifetime, in years.Round parameters to the nearest hundredth.
A)
B)
C)
D)
E)
Compute the linear regression equation for these data, where x is the age, in years, and A is the remaining lifetime, in years.Round parameters to the nearest hundredth.A)
B)
C)
D)
E)
Question
The simple interest on an investment is directly proportional to the amount of the investment.By investing $5750 in a certain certificate of deposit, you obtained an interest payment of $172.50 after 1 year.Determine a mathematical model that gives the interest, I, for this CD after 1 year in terms of the amount invested, P.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Question
A motorcycle was purchased for $39,000.Assuming the motorcycle depreciates at a rate of $4680 per year (straight-line depreciation) for the first 7 years, write the value v of the motorcycle as a function of the time t (measured in years) for 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Assume that y is directly proportional to x.If 
and 
, determine a linear model that relates y and x.
A)
B)
C)
D)
E)
and , determine a linear model that relates y and x.A)
B)
C)
D)
E)
Question
The sales tax on an item with a retail price of $908 is $99.88.Create a mathematical model that gives the retail price, y, in terms of the sales tax, x, and use it to determine the retail price of an item that has a sales tax of $113.50.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Graph y as a function of x by finding the slope and y-intercept of the line below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use the intercept form to find the equation of the line with the given intercepts.The intercept form of the equation of a line with intercepts (a, 0) and (0, b) is 
x-intercept: (3, 0) y-intercept: (0, 5)
A) 5x + 3y = 1
B)
C)
D) 3x + 5y = 15
E) 5x + 3y = 15
x-intercept: (3, 0) y-intercept: (0, 5)A) 5x + 3y = 1
B)
C)
D) 3x + 5y = 15
E) 5x + 3y = 15
Question
An open box is to be made from a square piece of cardboard having dimensions 34 inches by 34 inches by cutting out squares of area 
from each corner as shown in the figure below.If the volume of the box is given by 
state the domain of V . 
A)
B)
C)
D)
E) all real numbers
from each corner as shown in the figure below.If the volume of the box is given by state the domain of V . A)
B)
C)
D)
E) all real numbers
Question
Which graph represents the function? 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Question
An open box is to be made from a square piece of cardboard having dimensions 20 inches by 20 inches by cutting out squares of area 
from each corner as shown in the figure below.Express the volume V of the box as a function of x. 
A)
B)
C)
D)
E)
from each corner as shown in the figure below.Express the volume V of the box as a function of x. A)
B)
C)
D)
E)
Question
Find all real values of x such that f (x) = 0. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
The marketing department of a company estimates that the demand for a product is given by 
where 
is the price per unit and 
is the number of units.The cost 
of producing 
units is given by 
and the profit 
for producing and selling 
units is given by 
Sketch the graph of the profit function and estimate the number of units that would produce a maximum profit.
A) 590,000 units
B) 600,000 units
C) 640,000 units
D) 520,000 units
E) 620,000 units
where is the price per unit and is the number of units.The cost of producing units is given by and the profit for producing and selling units is given by Sketch the graph of the profit function and estimate the number of units that would produce a maximum profit.A) 590,000 units
B) 600,000 units
C) 640,000 units
D) 520,000 units
E) 620,000 units
Question
Given 
find 
A)
B)
C)
D)
E)
find A)
B)
C)
D)
E)
Question
Given 
find 
A) 320
B) -41
C) 321
D) -81
E) 319
find A) 320
B) -41
C) 321
D) -81
E) 319
Question
The inventor of a new game believes that the variable cost of producing the game is $3.65 per unit and the fixed costs are $5000.The inventor sells each game for $11.09.Let 
be the number of games sold.Write the average cost per unit 
as a function of 
where 
is defined as the total cost of producing 
games.
A)
B)
C)
D)
E)
be the number of games sold.Write the average cost per unit as a function of where is defined as the total cost of producing games.A)
B)
C)
D)
E)
Question
Question
Find the domain of the function. 
A) all real numbers
B) all real numbers
, 
C) all real numbers
D) s = -1, s = 0
E) s = -1
A) all real numbers
B) all real numbers
, C) all real numbers
D) s = -1, s = 0
E) s = -1
Question
Find the domain of the function. 
A) -9 < y 9
B) y -9 or y 9
C) y 0
D) y 9
E) all real numbers
A) -9 < y 9
B) y -9 or y 9
C) y 0
D) y 9
E) all real numbers
Question
Use the vertical line test to determine if the following graph is the graph of a function. 
A) function
B) not a function
A) function
B) not a function
Question
Question
Sketch the graph of the function below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find all real values of x such that f (x) = 0. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Suppose the average remaining lifetime for women in a given country is given in the following table. 
Find the linear regression equation for these data, whose parameters are rounded to the nearest hundredth, where x is the age, in years, and A is the remaining lifetime, in years.Use the regression equation to estimate the remaining lifetime for a 30-year old woman.
A) 59.79 years
B) 43.45 years
C) 49.47 years
D) 52.05 years
E) 57.21 years
Find the linear regression equation for these data, whose parameters are rounded to the nearest hundredth, where x is the age, in years, and A is the remaining lifetime, in years.Use the regression equation to estimate the remaining lifetime for a 30-year old woman.A) 59.79 years
B) 43.45 years
C) 49.47 years
D) 52.05 years
E) 57.21 years
Question
Use the graph of the function to find the domain and range of f. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
The national defense budget expenses 
(in billions of dollars) for veterans in the United States from 1990 to 2005 can be approximated by the model 
where 
represents the year, with 
corresponding to 1990.Use the model to find total veteran expenses in 2002.
A) $51.904 billion
B) $51.344 billion
C) $12.404 billion
D) $37.550 billion
E) $30.100 billion
(in billions of dollars) for veterans in the United States from 1990 to 2005 can be approximated by the model where represents the year, with corresponding to 1990.Use the model to find total veteran expenses in 2002.A) $51.904 billion
B) $51.344 billion
C) $12.404 billion
D) $37.550 billion
E) $30.100 billion
Question
Given 
find 
A) 33
B) 21
C) 45
D) 36
E) 27
find A) 33
B) 21
C) 45
D) 36
E) 27
Question
Evaluate the function at each specified value of the independent variable. 
a) 
b) 
c) 
d) 
A) 2, 2, -3, -4
B) 2, 3, -3, -4
C) 2, 2, -2, -4
D) 2, 2.5, 2.5, 4
E) 2, 2.5, -2.5, -4
a) b) c) d) A) 2, 2, -3, -4
B) 2, 3, -3, -4
C) 2, 2, -2, -4
D) 2, 2.5, 2.5, 4
E) 2, 2.5, -2.5, -4
Question
Use a graphing utility to graph the function and determine whether the function is even, odd, or neither. 
A) Neither even nor odd
B) Odd
C) Even
D) Neither even nor odd
E) Even
A) Neither even nor odd
B) Odd
C) Even
D) Neither even nor odd
E) Even
Question
Use the graph of 
to sketch the graph of 
A) Horizontal shift 2 units to the right
B) Reflection in the x-axis
C) Vertical shift 2 units upward
D) Horizontal shift 3 units to the left
E) Stretching by 2
to sketch the graph of A) Horizontal shift 2 units to the right
B) Reflection in the x-axis
C) Vertical shift 2 units upward
D) Horizontal shift 3 units to the left
E) Stretching by 2
Question
Identify the transformation shown in the graph and identify the associated common function.Write the equation of the graphed function. 
A) Common function:
Transformation: horizontal shift 2 units to the right
Equation:
B) Common function:
Transformation: multiplied by
shrinking
Equation:
C) Common function:
Transformation: reflection about the x-axis
Equation:
D) Common function:
Transformation:
is 7.
Equation:
E) Common function:
Transformation: reflection about the x-axis and a vertical shift 1 unit upward
Equation:
A) Common function:
Transformation: horizontal shift 2 units to the right
Equation:
B) Common function:
Transformation: multiplied by
shrinkingEquation:
C) Common function:
Transformation: reflection about the x-axis
Equation:
D) Common function:
Transformation:
is 7.Equation:
E) Common function:
Transformation: reflection about the x-axis and a vertical shift 1 unit upward
Equation:
Question
Use the graph of 
to write equations for the functions whose graphs are shown. 
A)
B)
C)
D)
E)
to write equations for the functions whose graphs are shown. A)
B)
C)
D)
E)
Question
Describe the sequence of transformation from 
to 
if 
A) Shifted five units to the left and six units downwards.
B) Shifted six units to the left and five units downwards.
C) Shifted five units to the right and six units upwards.
D) Shifted six units to the right and five units downwards.
E) Shifted five units to the left and six units upwards.
to if A) Shifted five units to the left and six units downwards.
B) Shifted six units to the left and five units downwards.
C) Shifted five units to the right and six units upwards.
D) Shifted six units to the right and five units downwards.
E) Shifted five units to the left and six units upwards.
Question
Describe the increasing, decreasing, and constant behavior of the function.Find the point or points where the behavior of the function changes. 
A) Increasing on
No change in the graph's behaviour
B) Decreasing on
Incresing on
The graph's behaviour changes at the point
C) Increasing on
and 
Decresing on
The graph's behaviour changes at the points
and 
D) Decreasing on
Increasing on
The graph's behaviour changes at the points
and 
E) Decreasing on
Incresing on
The graph's behaviour changes at the point
A) Increasing on
No change in the graph's behaviour
B) Decreasing on
Incresing on
The graph's behaviour changes at the point
C) Increasing on
and Decresing on
The graph's behaviour changes at the points
and D) Decreasing on
Increasing on
The graph's behaviour changes at the points
and E) Decreasing on
Incresing on
The graph's behaviour changes at the point
Question
Use a graphing utility to graph the function, approximate the relative minimum or maximum of the function, and estimate the open intervals on which the function is increasing or decreasing. 
A)
Decreasing on
Increasing on
Relative minimum:
B)
Decreasing on 
Increasing on
Relative maximum:
C)
Decreasing on 
Increasing on
Relative minimum:
Relative maximum:
D)
Decreasing on 
Increasing on
Relative minimum:
Relative maximum:
E)
Decreasing on 
Increasing on
Relative minimum:
Relative maximum:
A)
Decreasing on
Increasing on
Relative minimum:
B)
Decreasing on Increasing on
Relative maximum:
C)
Decreasing on Increasing on
Relative minimum:
Relative maximum:
D)
Decreasing on Increasing on
Relative minimum:
Relative maximum:
E)
Decreasing on Increasing on
Relative minimum:
Relative maximum:
Question
The weekly profit 
(in hundreds of dollars) for a business from a product is given by the model 
where 
is the amount (in hundreds of dollars) spent on advertising.Rewrite the profit equation so that 
measures advertising expenditures in dollars.
A)
B)
C)
D)
E)
(in hundreds of dollars) for a business from a product is given by the model where is the amount (in hundreds of dollars) spent on advertising.Rewrite the profit equation so that measures advertising expenditures in dollars.A)
B)
C)
D)
E)
Question
Describe the sequence of transformations from 
to 
Then sketch the graph of 
by hand.Verify with a graphing utility. 
A) Vertical shifts down 3 units
B) Vertical shifts 2 units upward
C) Horizontal shift 1 unit to the right
D) Horizontal shifts 4 units to the left
E) Vertical shifts 3 units upward
to Then sketch the graph of by hand.Verify with a graphing utility. A) Vertical shifts down 3 units
B) Vertical shifts 2 units upward
C) Horizontal shift 1 unit to the right
D) Horizontal shifts 4 units to the left
E) Vertical shifts 3 units upward
Question
Decide whether the function is even, odd, or neither. 
A) Odd
B) Even
C) Neither even nor odd
A) Odd
B) Even
C) Neither even nor odd
Question
Consider the graph of 
Use your knowledge of rigid and nonrigid transformations to write an equation for the following descriptions. The graph of 
is shifted three units to the left.
A)
B)
C)
D)
E)
Use your knowledge of rigid and nonrigid transformations to write an equation for the following descriptions. The graph of is shifted three units to the left.A)
B)
C)
D)
E)
Question
Sketch the graph of the function and determine whether the function is even, odd, or neither. 
A) Neither even nor odd
B)
Even 
C) Odd
D) Odd
E) Neither even nor odd
A) Neither even nor odd
B)
Even C) Odd
D) Odd
E) Neither even nor odd
Question
Describe the sequence of transformations from 
to 
Then sketch the graph of 
by hand.Verify with a graphing utility. 
A) Shifted 5 units downward
B) Shifted 1 unit upward
C) Shifted 4 units to the left
D) Shifts 3 units to the right
E) 4 units to the left and 2 units upward
to Then sketch the graph of by hand.Verify with a graphing utility. A) Shifted 5 units downward
B) Shifted 1 unit upward
C) Shifted 4 units to the left
D) Shifts 3 units to the right
E) 4 units to the left and 2 units upward
Question
Sketch the graph of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Consider the graph of 
Use your knowledge of rigid and nonrigid transformations to write an equation for the following descriptions. The graph of 
is reflected in the x-axis, shifted five units to the left, and shifted four unit upward.
A)
B)
C)
D)
E)
Use your knowledge of rigid and nonrigid transformations to write an equation for the following descriptions. The graph of is reflected in the x-axis, shifted five units to the left, and shifted four unit upward.A)
B)
C)
D)
E)
Question
Use the graph of 
to write an equation for the function whose graph is shown. 
A)
B)
C)
D)
E)
to write an equation for the function whose graph is shown. A)
B)
C)
D)
E)
Question
The cost of sending an overnight package from New York to Atlanta is $9.80 for up to, but not including, the first pound and $3.50 for each additional pound (or portion of a pound).A model for the total cost 
of sending the package is 
where 
is the weight of the package (in pounds).Sketch the graph of this function. Note that the function 
is the greatest integer function.
A)
B)
C)
D)
E)
of sending the package is where is the weight of the package (in pounds).Sketch the graph of this function. Note that the function is the greatest integer function.A)
B)
C)
D)
E)
Question
Sketch the graph of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use the graph of 
to write an equation for the function whose graphs is shown below. 
A)
B)
C)
D)
E)
to write an equation for the function whose graphs is shown below. A)
B)
C)
D)
E)
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Deck 2: Functions and Graphs
1
Assuming that the graph shown has y-axis symmetry, sketch the complete graph.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
A
2
Find the distance between the points.Round to the nearest hundredth, if necessary. (9, 2), (5, 5)
A) 15.65
B) 14.32
C) 5
D) 8.06
E) 7
A) 15.65
B) 14.32
C) 5
D) 8.06
E) 7
C
3
Given , use the algebraic tests to determine symmetry with respect to both axes and the origin.
A) y-axis symmetry only
B) x-axis symmetry only
C) origin symmetry only
D) x-axis, y-axis, and origin symmetry
E) no symmetry
, use the algebraic tests to determine symmetry with respect to both axes and the origin.A) y-axis symmetry only
B) x-axis symmetry only
C) origin symmetry only
D) x-axis, y-axis, and origin symmetry
E) no symmetry
C
4
Estimate the slope of the line.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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5
Given , use the algebraic tests to determine symmetry with respect to both axes and the origin.
A) y-axis symmetry only
B) x-axis symmetry only
C) origin symmetry only
D) x-axis, y-axis, and origin symmetry
E) no symmetry
, use the algebraic tests to determine symmetry with respect to both axes and the origin.A) y-axis symmetry only
B) x-axis symmetry only
C) origin symmetry only
D) x-axis, y-axis, and origin symmetry
E) no symmetry
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6
Find the midpoint of the line segment joining the points. (7, -7), (-7, -5)
A) (0, 6)
B) (-6, 0)
C) (-1, 7)
D) (7, -1)
E) (0, -6)
A) (0, 6)
B) (-6, 0)
C) (-1, 7)
D) (7, -1)
E) (0, -6)
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7
Find the x- and y-intercepts of the graph of the equation below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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8
Plot the points below whose coordinates are given on a Cartesian coordinate system.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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9
Find an equation of a circle that satisfies the following condition.Write your answer in standard form. Center: ; passing through
A)
B)
C)
D)
E)
; passing through A)
B)
C)
D)
E)
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10
Graph the following equation by plotting points that satisfy the equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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11
Sketch the graph of the equation below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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12
The population (in millions of people) of North America from 1980 to 2050 can be modeled by where represents the year, with corresponding to 2050.Find the y-intercept of the graph of the model.What does it represent in the given situation?
A) It represents the population (in millions of people) of North America in 2050.
B) It represents the population (in millions of people) of North America in 1990.
C) It represents the population (in millions of people) of North America in 2030.
D) It represents the population (in millions of people) of North America in 2020.
E) It represents the population (in millions of people) of North America in 1980.
(in millions of people) of North America from 1980 to 2050 can be modeled by where represents the year, with corresponding to 2050.Find the y-intercept of the graph of the model.What does it represent in the given situation?A)
It represents the population (in millions of people) of North America in 2050.B)
It represents the population (in millions of people) of North America in 1990.C)
It represents the population (in millions of people) of North America in 2030.D)
It represents the population (in millions of people) of North America in 2020.E)
It represents the population (in millions of people) of North America in 1980. Unlock Deck
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13
Find the x- and y-intercepts of the graph of the following equation.
A) x-int: ; y-int:
B) x-int: ; y-int:
C) x-int: ; y-int:
D) x-int: ; y-int:
E) x-int: ; y-int:
A) x-int:
; y-int: B) x-int:
; y-int: C) x-int:
; y-int: D) x-int:
; y-int: E) x-int:
; y-int: Unlock Deck
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14
Write the standard form of the equation of the circle whose diameter has endpoints of and
A)
B)
C)
D)
E)
and A)
B)
C)
D)
E)
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15
Find the slope of the line that passes through the points and
A) 9
B) -5
C) 5
D) 0
E) undefined
and A) 9
B) -5
C) 5
D) 0
E) undefined
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16
Find such that the distance between the point and is 10.
A)
B)
C)
D)
E)
such that the distance between the point and is 10.A)
B)
C)
D)
E)
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17
After completing the table, use the resulting solution points to sketch the graph of the equation
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18
Plot the points and find the slope of the line passing through the pair of points. (2, -4), (4, -1)
A) slope:
B) slope:
C) slope:
D) slope:
E) slope:
A) slope:
B) slope:
C) slope:
D) slope:
E) slope:
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19
Sketch the graph of the equation below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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20
Match the equation below with its graph. Graph I : Graph IV : Graph II : Graph V : Graph III :
A) Graph IV
B) Graph III
C) Graph V
D) Graph II
E) Graph I
Graph I : Graph IV : Graph II : Graph V : Graph III : A) Graph IV
B) Graph III
C) Graph V
D) Graph II
E) Graph I
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21
After opening the parachute, the descent of a parachutist follows a linear model.At 7:28 P.M., the height of the parachutist is 6150 feet.At 7:31 P.M., the height is 3450 feet.Use a linear equation that gives the height of the parachutist in terms of the time to find the time when the parachutist will reach the ground.
A) 7:33:30 P.M.
B) 7:34:50 P.M.
C) 7:32:00 P.M.
D) 7:37:30 P.M.
E) 7:31:00 P.M.
A) 7:33:30 P.M.
B) 7:34:50 P.M.
C) 7:32:00 P.M.
D) 7:37:30 P.M.
E) 7:31:00 P.M.
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22
The table below shows the velocities, in feet per second, of a ball that is thrown horizontally from the top of a 50 foot building and the distances, in feet, that it lands from the base of the building.Compute the linear regression equation for these data.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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23
Find the slope of the line that passes through the points
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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24
Use the point on the line and the slope of the line to determine whether any of the three additional points lies on the line. Point
Slope I: II: III:
A) Only point I lies on the line.
B) None of the points lies on the line.
C) Only point III lies on the line.
D) Only points I and II lie on the line.
E) Only points I and III lie on the line.
Slope
I: II: III: A) Only point I lies on the line.
B) None of the points lies on the line.
C) Only point III lies on the line.
D) Only points I and II lie on the line.
E) Only points I and III lie on the line.
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25
Determine if lines and are parallel, perpendicular, or neither.
A) parallel
B) neither
C) perpendicular
and are parallel, perpendicular, or neither. A) parallel
B) neither
C) perpendicular
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26
Determine whether lines L1 and L2 passing through the pairs of points are parallel, perpendicular, or neither. L1 : (-1, 8), (9, -4)
L2 : (0, 9), (1, -1)
A) parallel
B) perpendicular
C) neither
L2 : (0, 9), (1, -1)
A) parallel
B) perpendicular
C) neither
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27
Determine whether lines L1 and L2 passing through the pairs of points are parallel, perpendicular, or neither. L1 : (1, 2), (1, 4)
L2 : (-7, -8), (-9, -8)
A) parallel
B) perpendicular
C) neither
L2 : (-7, -8), (-9, -8)
A) parallel
B) perpendicular
C) neither
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28
Determine whether lines L1 and L2 passing through the pairs of points are parallel, perpendicular, or neither. L1 : (-5, -5), (4, 6)
L2 : (-9, 8), (-18, -3)
A) parallel
B) perpendicular
C) neither
L2 : (-9, 8), (-18, -3)
A) parallel
B) perpendicular
C) neither
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29
Find the slope and y-intercept of the equation of the line.
A) slope: ; y-intercept: 4
B) slope: ; y-intercept: -6
C) slope: -6; y-intercept: 4
D) slope: 4; y-intercept: -6
E) slope: -6; y-intercept: -4
A) slope:
; y-intercept: 4B) slope:
; y-intercept: -6C) slope: -6; y-intercept: 4
D) slope: 4; y-intercept: -6
E) slope: -6; y-intercept: -4
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30
Plot the points and find the slope of the line passing through the pair of points. (3, -2), (-4, -2)
A) slope: 0
B) slope: 1
C) slope: -7
D) slope:
E) slope: undefined
A) slope: 0
B) slope: 1
C) slope: -7
D) slope:
E) slope: undefined
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31
Which of the following graphs below can be approximated by a linear model? I II III
A) None can be modeled linearly.
B) Only graphs II and III can be modeled linearly.
C) Only graph III can be modeled linearly.
D) Only graphs I and II can be modeled linearly.
E) Only graph I can be modeled linearly.
II III A) None can be modeled linearly.
B) Only graphs II and III can be modeled linearly.
C) Only graph III can be modeled linearly.
D) Only graphs I and II can be modeled linearly.
E) Only graph I can be modeled linearly.
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32
Write the equation that expresses the relationship between the variables described below, then use the given data to solve for the variation of constant. "t varies directly as , and when "
A) ;
B) ;
C) ;
D) ;
E) ;
, and when "A)
; B)
; C)
; D)
; E)
; Unlock Deck
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33
Suppose the average remaining lifetime for women in a given country is given in the following table. Compute the linear regression equation for these data, where x is the age, in years, and A is the remaining lifetime, in years.Round parameters to the nearest hundredth.
A)
B)
C)
D)
E)
Compute the linear regression equation for these data, where x is the age, in years, and A is the remaining lifetime, in years.Round parameters to the nearest hundredth.A)
B)
C)
D)
E)
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34
The simple interest on an investment is directly proportional to the amount of the investment.By investing $5750 in a certain certificate of deposit, you obtained an interest payment of $172.50 after 1 year.Determine a mathematical model that gives the interest, I, for this CD after 1 year in terms of the amount invested, P.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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35
Find the slope and y-intercept of the equation of the line. -y - 8x = -2
A) slope: 8; y-intercept: -2
B) slope: -2; y-intercept: 8
C) slope: 8; y-intercept: -1
D) slope: 2; y-intercept: -8
E) slope: -8; y-intercept: 2
A) slope: 8; y-intercept: -2
B) slope: -2; y-intercept: 8
C) slope: 8; y-intercept: -1
D) slope: 2; y-intercept: -8
E) slope: -8; y-intercept: 2
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36
A motorcycle was purchased for $39,000.Assuming the motorcycle depreciates at a rate of $4680 per year (straight-line depreciation) for the first 7 years, write the value v of the motorcycle as a function of the time t (measured in years) for
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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37
Assume that y is directly proportional to x.If and , determine a linear model that relates y and x.
A)
B)
C)
D)
E)
and , determine a linear model that relates y and x.A)
B)
C)
D)
E)
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38
The sales tax on an item with a retail price of $908 is $99.88.Create a mathematical model that gives the retail price, y, in terms of the sales tax, x, and use it to determine the retail price of an item that has a sales tax of $113.50.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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39
Graph y as a function of x by finding the slope and y-intercept of the line below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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40
Use the intercept form to find the equation of the line with the given intercepts.The intercept form of the equation of a line with intercepts (a, 0) and (0, b) is x-intercept: (3, 0) y-intercept: (0, 5)
A) 5x + 3y = 1
B)
C)
D) 3x + 5y = 15
E) 5x + 3y = 15
x-intercept: (3, 0) y-intercept: (0, 5)A) 5x + 3y = 1
B)
C)
D) 3x + 5y = 15
E) 5x + 3y = 15
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41
An open box is to be made from a square piece of cardboard having dimensions 34 inches by 34 inches by cutting out squares of area from each corner as shown in the figure below.If the volume of the box is given by state the domain of V .
A)
B)
C)
D)
E) all real numbers
from each corner as shown in the figure below.If the volume of the box is given by state the domain of V . A)
B)
C)
D)
E) all real numbers
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42
Which graph represents the function?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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43
Use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values. f (x) = x3 + 2x2 + x - 5
A) relative maximum: (-1.00, -5.00)
Relative minimum: (-0.33, -5.15)
B) relative maximum: (-0.33, -5.15)
Relative minimum: (-1.00, -5.00)
C) relative maximum: (-5.00, -1.00)
Relative minimum: (-5.15, -0.33)
D) relative maximum: (-5.15, -0.33)
Relative minimum: (-5.00, -1.00)
E) relative maximum: (-5.15, -93.58)
Relative minimum: (-5.00, -85.00)
A) relative maximum: (-1.00, -5.00)
Relative minimum: (-0.33, -5.15)
B) relative maximum: (-0.33, -5.15)
Relative minimum: (-1.00, -5.00)
C) relative maximum: (-5.00, -1.00)
Relative minimum: (-5.15, -0.33)
D) relative maximum: (-5.15, -0.33)
Relative minimum: (-5.00, -1.00)
E) relative maximum: (-5.15, -93.58)
Relative minimum: (-5.00, -85.00)
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44
An open box is to be made from a square piece of cardboard having dimensions 20 inches by 20 inches by cutting out squares of area from each corner as shown in the figure below.Express the volume V of the box as a function of x.
A)
B)
C)
D)
E)
from each corner as shown in the figure below.Express the volume V of the box as a function of x. A)
B)
C)
D)
E)
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45
Find all real values of x such that f (x) = 0.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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46
The marketing department of a company estimates that the demand for a product is given by where is the price per unit and is the number of units.The cost of producing units is given by and the profit for producing and selling units is given by Sketch the graph of the profit function and estimate the number of units that would produce a maximum profit.
A) 590,000 units
B) 600,000 units
C) 640,000 units
D) 520,000 units
E) 620,000 units
where is the price per unit and is the number of units.The cost of producing units is given by and the profit for producing and selling units is given by Sketch the graph of the profit function and estimate the number of units that would produce a maximum profit.A) 590,000 units
B) 600,000 units
C) 640,000 units
D) 520,000 units
E) 620,000 units
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47
Given find
A)
B)
C)
D)
E)
find A)
B)
C)
D)
E)
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48
Given find
A) 320
B) -41
C) 321
D) -81
E) 319
find A) 320
B) -41
C) 321
D) -81
E) 319
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49
The inventor of a new game believes that the variable cost of producing the game is $3.65 per unit and the fixed costs are $5000.The inventor sells each game for $11.09.Let be the number of games sold.Write the average cost per unit as a function of where is defined as the total cost of producing games.
A)
B)
C)
D)
E)
be the number of games sold.Write the average cost per unit as a function of where is defined as the total cost of producing games.A)
B)
C)
D)
E)
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50
Evaluate the function at the specified value of the independent variable and simplify. f (y) = 6y + 3; f (0.8)
A) 4.8y + 18
B) 1.8
C) 7.8
D) 0.8y + 3
E) 0.8y - 3
A) 4.8y + 18
B) 1.8
C) 7.8
D) 0.8y + 3
E) 0.8y - 3
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51
Find the domain of the function.
A) all real numbers
B) all real numbers ,
C) all real numbers
D) s = -1, s = 0
E) s = -1
A) all real numbers
B) all real numbers
, C) all real numbers
D) s = -1, s = 0
E) s = -1
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52
Find the domain of the function.
A) -9 < y 9
B) y -9 or y 9
C) y 0
D) y 9
E) all real numbers
A) -9 < y 9
B) y -9 or y 9
C) y 0
D) y 9
E) all real numbers
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53
Use the vertical line test to determine if the following graph is the graph of a function.
A) function
B) not a function
A) function
B) not a function
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54
Which set of ordered pairs represents a function from P to Q? P = {5, 10, 15, 20} Q = {-1, 1, 3}
A) {(5, -1), (10, 1), (10, 3), (15, 1), (20, -1)}
B) {(15, -1), (15, 1), (15, 3)}
C) {(15, 1), (10, -1), (5, 1), (10, 3), (15, -1)}
D) {(10, 1), (15, 3), (20, 1)}
E) {(5, 3), (15, 1), (5, -1), (15, 3)}
A) {(5, -1), (10, 1), (10, 3), (15, 1), (20, -1)}
B) {(15, -1), (15, 1), (15, 3)}
C) {(15, 1), (10, -1), (5, 1), (10, 3), (15, -1)}
D) {(10, 1), (15, 3), (20, 1)}
E) {(5, 3), (15, 1), (5, -1), (15, 3)}
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55
Sketch the graph of the function below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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56
Find all real values of x such that f (x) = 0.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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57
Suppose the average remaining lifetime for women in a given country is given in the following table. Find the linear regression equation for these data, whose parameters are rounded to the nearest hundredth, where x is the age, in years, and A is the remaining lifetime, in years.Use the regression equation to estimate the remaining lifetime for a 30-year old woman.
A) 59.79 years
B) 43.45 years
C) 49.47 years
D) 52.05 years
E) 57.21 years
Find the linear regression equation for these data, whose parameters are rounded to the nearest hundredth, where x is the age, in years, and A is the remaining lifetime, in years.Use the regression equation to estimate the remaining lifetime for a 30-year old woman.A) 59.79 years
B) 43.45 years
C) 49.47 years
D) 52.05 years
E) 57.21 years
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58
Use the graph of the function to find the domain and range of f.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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59
The national defense budget expenses (in billions of dollars) for veterans in the United States from 1990 to 2005 can be approximated by the model where represents the year, with corresponding to 1990.Use the model to find total veteran expenses in 2002.
A) $51.904 billion
B) $51.344 billion
C) $12.404 billion
D) $37.550 billion
E) $30.100 billion
(in billions of dollars) for veterans in the United States from 1990 to 2005 can be approximated by the model where represents the year, with corresponding to 1990.Use the model to find total veteran expenses in 2002.A) $51.904 billion
B) $51.344 billion
C) $12.404 billion
D) $37.550 billion
E) $30.100 billion
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60
Given find
A) 33
B) 21
C) 45
D) 36
E) 27
find A) 33
B) 21
C) 45
D) 36
E) 27
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61
Evaluate the function at each specified value of the independent variable. a) b) c) d)
A) 2, 2, -3, -4
B) 2, 3, -3, -4
C) 2, 2, -2, -4
D) 2, 2.5, 2.5, 4
E) 2, 2.5, -2.5, -4
a) b) c) d) A) 2, 2, -3, -4
B) 2, 3, -3, -4
C) 2, 2, -2, -4
D) 2, 2.5, 2.5, 4
E) 2, 2.5, -2.5, -4
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62
Use a graphing utility to graph the function and determine whether the function is even, odd, or neither.
A) Neither even nor odd
B) Odd
C) Even
D) Neither even nor odd
E) Even
A) Neither even nor odd
B) Odd
C) Even
D) Neither even nor odd
E) Even
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63
Use the graph of to sketch the graph of
A) Horizontal shift 2 units to the right
B) Reflection in the x-axis
C) Vertical shift 2 units upward
D) Horizontal shift 3 units to the left
E) Stretching by 2
to sketch the graph of A) Horizontal shift 2 units to the right
B) Reflection in the x-axis
C) Vertical shift 2 units upward
D) Horizontal shift 3 units to the left
E) Stretching by 2
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64
Identify the transformation shown in the graph and identify the associated common function.Write the equation of the graphed function.
A) Common function:
Transformation: horizontal shift 2 units to the right
Equation:
B) Common function:
Transformation: multiplied by shrinking
Equation:
C) Common function:
Transformation: reflection about the x-axis
Equation:
D) Common function:
Transformation: is 7.
Equation:
E) Common function:
Transformation: reflection about the x-axis and a vertical shift 1 unit upward
Equation:
A) Common function:
Transformation: horizontal shift 2 units to the right
Equation:
B) Common function:
Transformation: multiplied by
shrinkingEquation:
C) Common function:
Transformation: reflection about the x-axis
Equation:
D) Common function:
Transformation:
is 7.Equation:
E) Common function:
Transformation: reflection about the x-axis and a vertical shift 1 unit upward
Equation:
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65
Use the graph of to write equations for the functions whose graphs are shown.
A)
B)
C)
D)
E)
to write equations for the functions whose graphs are shown. A)
B)
C)
D)
E)
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Unlock Deck
k this deck
66
Describe the sequence of transformation from to if
A) Shifted five units to the left and six units downwards.
B) Shifted six units to the left and five units downwards.
C) Shifted five units to the right and six units upwards.
D) Shifted six units to the right and five units downwards.
E) Shifted five units to the left and six units upwards.
to if A) Shifted five units to the left and six units downwards.
B) Shifted six units to the left and five units downwards.
C) Shifted five units to the right and six units upwards.
D) Shifted six units to the right and five units downwards.
E) Shifted five units to the left and six units upwards.
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67
Describe the increasing, decreasing, and constant behavior of the function.Find the point or points where the behavior of the function changes.
A) Increasing on
No change in the graph's behaviour
B) Decreasing on
Incresing on
The graph's behaviour changes at the point
C) Increasing on and
Decresing on
The graph's behaviour changes at the points and
D) Decreasing on
Increasing on
The graph's behaviour changes at the points and
E) Decreasing on
Incresing on
The graph's behaviour changes at the point
A) Increasing on
No change in the graph's behaviour
B) Decreasing on
Incresing on
The graph's behaviour changes at the point
C) Increasing on
and Decresing on
The graph's behaviour changes at the points
and D) Decreasing on
Increasing on
The graph's behaviour changes at the points
and E) Decreasing on
Incresing on
The graph's behaviour changes at the point
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68
Use a graphing utility to graph the function, approximate the relative minimum or maximum of the function, and estimate the open intervals on which the function is increasing or decreasing.
A)
Decreasing on
Increasing on
Relative minimum:
B) Decreasing on
Increasing on
Relative maximum:
C) Decreasing on
Increasing on
Relative minimum:
Relative maximum:
D) Decreasing on
Increasing on
Relative minimum:
Relative maximum:
E) Decreasing on
Increasing on
Relative minimum:
Relative maximum:
A)
Decreasing on
Increasing on
Relative minimum:
B)
Decreasing on Increasing on
Relative maximum:
C)
Decreasing on Increasing on
Relative minimum:
Relative maximum:
D)
Decreasing on Increasing on
Relative minimum:
Relative maximum:
E)
Decreasing on Increasing on
Relative minimum:
Relative maximum:
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k this deck
69
The weekly profit (in hundreds of dollars) for a business from a product is given by the model where is the amount (in hundreds of dollars) spent on advertising.Rewrite the profit equation so that measures advertising expenditures in dollars.
A)
B)
C)
D)
E)
(in hundreds of dollars) for a business from a product is given by the model where is the amount (in hundreds of dollars) spent on advertising.Rewrite the profit equation so that measures advertising expenditures in dollars.A)
B)
C)
D)
E)
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Unlock Deck
k this deck
70
Describe the sequence of transformations from to Then sketch the graph of by hand.Verify with a graphing utility.
A) Vertical shifts down 3 units
B) Vertical shifts 2 units upward
C) Horizontal shift 1 unit to the right
D) Horizontal shifts 4 units to the left
E) Vertical shifts 3 units upward
to Then sketch the graph of by hand.Verify with a graphing utility. A) Vertical shifts down 3 units
B) Vertical shifts 2 units upward
C) Horizontal shift 1 unit to the right
D) Horizontal shifts 4 units to the left
E) Vertical shifts 3 units upward
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Unlock Deck
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71
Decide whether the function is even, odd, or neither.
A) Odd
B) Even
C) Neither even nor odd
A) Odd
B) Even
C) Neither even nor odd
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Unlock Deck
k this deck
72
Consider the graph of Use your knowledge of rigid and nonrigid transformations to write an equation for the following descriptions. The graph of is shifted three units to the left.
A)
B)
C)
D)
E)
Use your knowledge of rigid and nonrigid transformations to write an equation for the following descriptions. The graph of is shifted three units to the left.A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
k this deck
73
Sketch the graph of the function and determine whether the function is even, odd, or neither.
A) Neither even nor odd
B) Even
C) Odd
D) Odd
E) Neither even nor odd
A) Neither even nor odd
B)
Even C) Odd
D) Odd
E) Neither even nor odd
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Unlock Deck
k this deck
74
Describe the sequence of transformations from to Then sketch the graph of by hand.Verify with a graphing utility.
A) Shifted 5 units downward
B) Shifted 1 unit upward
C) Shifted 4 units to the left
D) Shifts 3 units to the right
E) 4 units to the left and 2 units upward
to Then sketch the graph of by hand.Verify with a graphing utility. A) Shifted 5 units downward
B) Shifted 1 unit upward
C) Shifted 4 units to the left
D) Shifts 3 units to the right
E) 4 units to the left and 2 units upward
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Unlock Deck
k this deck
75
Sketch the graph of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
k this deck
76
Consider the graph of Use your knowledge of rigid and nonrigid transformations to write an equation for the following descriptions. The graph of is reflected in the x-axis, shifted five units to the left, and shifted four unit upward.
A)
B)
C)
D)
E)
Use your knowledge of rigid and nonrigid transformations to write an equation for the following descriptions. The graph of is reflected in the x-axis, shifted five units to the left, and shifted four unit upward.A)
B)
C)
D)
E)
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Unlock Deck
k this deck
77
Use the graph of to write an equation for the function whose graph is shown.
A)
B)
C)
D)
E)
to write an equation for the function whose graph is shown. A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 97 flashcards in this deck.
Unlock Deck
k this deck
78
The cost of sending an overnight package from New York to Atlanta is $9.80 for up to, but not including, the first pound and $3.50 for each additional pound (or portion of a pound).A model for the total cost of sending the package is where is the weight of the package (in pounds).Sketch the graph of this function. Note that the function is the greatest integer function.
A)
B)
C)
D)
E)
of sending the package is where is the weight of the package (in pounds).Sketch the graph of this function. Note that the function is the greatest integer function.A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
k this deck
79
Sketch the graph of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
k this deck
80
Use the graph of to write an equation for the function whose graphs is shown below.
A)
B)
C)
D)
E)
to write an equation for the function whose graphs is shown below. A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 97 flashcards in this deck.
Unlock Deck
k this deck
Unlock Deck
Unlock for access to all 97 flashcards in this deck.
