Deck 3: Polynomial and Rational Functions

Question 1

Find the vertex of the parabola.

Answer 1

C

Question 2

Find the vertex of the parabola.

Answer 2

D

Question 3

Graph the function.

Answer 3

A

Question 4

Choose the one alternative that best completes the statement or answers the question.
Determine whether the graph of the parabola opens upward or downward and determine the range.

Question 5

Find the vertex.

Question 6

Determine the x- and y-intercepts for the given function.

Question 7

Sketch the function and determine the axis of symmetry.

Question 8

Graph the function and determine the minimum or maximum value of the function.

Question 9

Given e parabola opened (upward/downward) and the
(minimum/maximum) value is .

Question 10

Identify the graph of the function.

Question 11

Identify the vertex and determine the minimum or maximum value of the function.

Question 12

Given he vertex of the parabola is the point .

Question 13

The vertical line drawn through the vertex of a quadratic function is called the of
symmetry.

Question 14

A function defined by 0) is called a function.

Question 15

Find the vertex of the parabola.

Question 16

Find the vertex.

Question 17

Graph the parabola and the axis of symmetry. Label the coordinates of the vertex, and write the
equation of the axis of symmetry.

Question 18

0, is a parabola and the axis of symmetry is a line given by
.

Question 19

Given e parabola opened (upward/downward) and the
(minimum/maximum) value is .

Question 20

Graph the function.

Question 21

Identify the vertex and determine the minimum or maximum value of the function.

Question 22

Find the vertex of the parabola by applying the vertex formula.

Question 23

Identify the vertex, axis of symmetry, and intercepts for the graph of the function.

Question 24

Determine the minimum or maximum value of the function.

Question 25

Identify the vertex, axis of symmetry, and intercepts for the graph of the function.

Question 26

Find the vertex of the parabola by applying the vertex formula.

Question 27

Write the domain and range of the function in interval notation.

Question 28

Determine the x- and y-intercepts for the given function.

Question 29

Sketch the function and determine the axis of symmetry.

Question 30

Write the function in vertex form and determine the x-intercept(s)

Question 31

Solve the problem.
The population P(t) of a culture of bacteria is given by where t is the time in hours since the culture was started. Determine the time at which the population is at a
Maximum. Round to the nearest hour.

A) 22 hr
B) 44 hr
C) 9 hr
D) 18 hr

Question 32

Write the function in vertex form and determine the x-intercept(s)

Question 33

Find the vertex of the parabola by applying the vertex formula.

Question 34

Identify the vertex, axis of symmetry, and intercepts for the graph of the function.

Question 35

Write the domain and range of the function in interval notation.

Question 36

Write the function in vertex form and determine the range.

Question 37

Identify the vertex and sketch the graph.

Question 38

Find the vertex of the parabola by applying the vertex formula.

Question 39

Identify the vertex, axis of symmetry, and intercepts for the graph of the function.

Question 40

Identify the vertex and sketch the graph.

Question 41

Find the value of c that gives the function the given minimum value.

A) -5
B) 5
C) c = -4
D) c = 6

Question 42

Solve the problem.
Gas mileage is tested for a car under different driving conditions. At lower speeds, the car is driven in stop and go traffic. At higher speeds, the car must overcome more wind resistance. The variable x
Given in the table represents the speed (in mph) for a compact car, and m(x) represents the gas mileage
(in mpg). Use regression to find a quadratic function to model the data.

Question 43

Solve the problem.

A) None
B) One
C) Two

Question 44

Solve the problem.
A trough at the end of a gutter spout is meant to direct water away from a house. The homeowner makes the trough from a rectangular piece of aluminum that is 24 in. long and 8 in. wide. He makes
A fold along the two long sides a distance of x inches from the edge.

Question 45

Find the value of b that gives the function the given maximum value.

Question 46

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
A quadratic function is a polynomial function of degree .

Question 47

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
A linear function is a polynomial function of degree .

Question 48

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.

Question 49

Solve the problem.
The monthly profit for a small company that makes long-sleeve T-shirts depends on the price per shirt. If the price is too high, sales will drop. If the price is too low, the revenue brought in may not
Cover the cost to produce the shirts. After months of data collection, the sales team determines that
The monthly profit is approximated by , where p is the price per shirt
And f p is the monthly profit based on that price. Find the price that generates the maximum profit
And find the maximum profit.

Question 50

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.

Question 51

Solve the problem.
A family wants to fence in a rectangular area for a garden. One side of the garden will border their house and will not be fenced. Find the dimensions of the garden with greatest area that can be
Enclosed with 80 ft of fencing.

A) 9 ft by 9 ft
B) 40 ft by 40 ft
C) 20 ft by 40 ft
D) 20 ft by 20 ft

Question 52

Solve the problem.
The daily profit in dollars made by an automobile manufacturer is where x is the number of cars produced per shift. Find the maximum possible daily profit.

A) $17,305
B) $20,315
C) $18,810
D) $15,989

Question 53

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.

Question 54

Solve the problem.
A fireworks mortar is launched straight upward from a pool deck platform 4 m off the ground at an initial velocity of 61 m/sec. The height of the mortar can be modeled by where h(t) is the height in meters and t is the time in seconds after launch. What is the maximum
Height? Round to the nearest meter.

A) 237 m
B) 4 m
C) 6 m
D) 194 m

Question 55

Solve the problem.
Gas mileage is tested for a car under different driving conditions. At lower speeds, the car is driven in stop and go traffic. At higher speeds, the car must overcome more wind resistance. The variable x
Given in the table represents the speed (in mph) for a compact car, and m(x) represents the gas mileage
(in mpg). Use regression to find a quadratic function to model the data and then use the function to determine
The speed with the greatest gas mileage. Round to the nearest mile per hour. Carry out all computations up to
The final answer without rounding.

Question 56

Solve the problem.
A model rocket is launched from a raised platform at a speed of 112 feet per second. Its height in feet is given by t = seconds after launch). After how many seconds does
The object reach its maximum height?

A) 5.5 seconds
B) 20 seconds
C) 1.75 seconds
D) 3.5 seconds

Question 57

Solve the problem.
Tetanus bacillus bacteria are cultured to produce tetanus toxin used in an inactive form for the
tetanus vaccine. The amount of toxin produced per batch increases with time and then decreases as
the culture becomes unstable. The variable t is the time in hours after the culture has started, and y
t is the yield of toxin in grams.

Question 58

Solve the problem.
The sum of two positive numbers is 26. What two numbers will maximize the product?

A) 11 and 15
B) 1 and 25
C) 13 and 13
D) -13 and 13

Question 59

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
Determine if the statement is true or false. The graph of the function defined by | is smooth.

Question 60

Solve the problem.
An automobile manufacturer can produce up to 300 cars per day. The profit made from the sale of these vehicles can be modeled by the function where P(x) is the
Profit in dollars and x is the number of automobiles made and sold. How many cars should be made
And sold to maximize profit?

A) 1,900
B) 95
C) 45
D) 190

Question 61

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
The end behavior of the graph of is (up/down) to the left and (up/down) to the right.

Question 62

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
If c is a real zero of a polynomial function and the multiplicity is 6, does the graph of the function
cross the x-axis or touch the x-axis (without crossing) at (c, 0)?

Question 63

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
The values of x in the domain of a polynomial function f for which are called the
of the function.

Question 64

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
Determine if the statement is true or false. The function defined by is continuous.

Question 65

Choose the one alternative that best completes the statement or answers the question.
Determine the end behavior of the graph of the function.

Question 66

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
The end behavior of the graph of is (up/down) to the left and (up/down) to the right.

Question 67

Find the zeros of the function and state the multiplicities.

Question 68

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
Suppose that f is a polynomial function and that a < b. If f(a) and f(b) have opposite signs, then what
conclusion can be drawn from the intermediate value theorem?

Question 69

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
Given the function defined by , the value 0 is a zero with multiplicity ,
and the value -0.6 is a zero with multiplicity .

Question 70

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
If the graph of a polynomial function has 3 turning points, what is the minimum degree of the
function?

Question 71

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
What is the maximum number of turning points of the graph of

Question 72

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
What is the leading term of ?

Question 73

Choose the one alternative that best completes the statement or answers the question.
Determine the end behavior of the graph of the function.

Question 74

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
What is the leading term of ?

Question 75

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
Given the function defined by , the value 1 is a zero with multiplicity
, and the value -5 is a zero with multiplicity .

Question 76

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
If c is a real zero of a polynomial function and the multiplicity is 3, does the graph of the function
cross the x-axis or touch the x-axis (without crossing) at (c, 0)?

Question 77

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
An even function is symmetric with respect to the axis.

Question 78

Choose the one alternative that best completes the statement or answers the question.
Determine the end behavior of the graph of the function.

Question 79

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
An odd function is symmetric with respect to the .

Question 80

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
If the leading term of a polynomial function is where a is negative and n is odd, determine the
end behavior.