Deck 1: Functions and Models

Question 1

If , find

Answer 1

Question 2

Find if

Answer 2

Question 3

Simplify the expression.

Answer 3

Question 4

Let and Find

Question 5

It makes sense that the larger the area of a region, the larger the number of species that inhabit the region.Many ecologists have modeled the species-area relation with a power function and, in particular, the number of species S of bats living in caves in central Mexico has been related to the surface area A measured in of the caves by the equation (a) The cave called mission impossible near puebla, mexico, has suface area of How many species of bats would expect to find in that cave? (b) If you discover that species of bats live in cave estimate the area of the cave.

Question 6

Let and Find

Question 7

Fill in the blanks.

Question 8

Find the points of intersection of the graphs of the functions.Express yourAnswers accurate to five decimal places.

Question 9

If find

Question 10

Refer to the graph of the function in the following figure.
a.Find b.Find the value of for which (i) c.Find the domain and range of

Question 11

Determine whether is even, odd, or neither.

Question 12

Solve each equation for x.

Question 13

Find the range of the function.

Question 14

The relationship between the Fahrenheit and Celsius temperature scales is given by the linear function. Complete the table and find the slope.

Question 15

Find the function such that and

Question 16

The graphs of are given.a) For what values of is b) Find the values of

Question 17

Plot the graph of the function in an appropriate viewing window.

Question 18

Plot the graph of the function in (a) the standard viewing window and (b) the indicated window.

Question 19

Determine whether is one-to-one.

Question 20

A spherical balloon with radius inches has volume Find a function that represents the amount of air required to inflate the balloon from a radius of inches to a radius of inches.

Question 21

Let and Find

Question 22

By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box can be made.If the cardboard is 13 in.long and 9 in.wide and the square cutaways have dimensions of in.by in., find a function that gives the volume of the resulting box.

Question 23

Determine whether the function is even, odd, or neither.

Question 24

Find the exact value of the expression.

Question 25

Determine whether is one-to-one.

Question 26

Find the function such that

Question 27

Refer to the graph of the function in the following figure.
a.Find b.Find the value of x for which (i) c.Find the domain and range of

Question 28

Find the points of intersection of the graphs of the functions.Express yourAnswers accurate to five decimal places.

Question 29

find

Question 30

Find the range of the function.

Question 31

Use the vertical line test to determine whether the curve is the graph of a function of

Question 32

Find all solutions of the equation correct to two decimal places.

Question 33

Find if

Question 34

Express the function in the form of

Question 35

Solve each equation for x.(a) (b)

Question 36

The graph of is given.Sketch the graph of on the same set of axes.

Question 37

Let and Find

Question 38

Find the inverse of Then sketch the graphs of and on the same set of axes.

Question 39

Plot the graph of the function in an appropriate viewing window.

Question 40

The following figure shows a portion of the graph of a function defined on the interval Sketch the complete graph of if it is known is odd.

Question 41

Select the correct Answer for each question.
Find the exact value of the given expression.

A)
B)
C)
D)

Question 42

Select the correct Answer for each question.
Simplify the expression.

A)9
B)18
C)216
D)729

Question 43

Select the correct Answer for each question.
Use the Law of Exponents to rewrite and simplify the expression.

A)
B)
C)
D)
E)

Question 44

Select the correct Answer for each question.
Which of the following graphs is the graph of the function?

A)Graph 2
B)Graph 1
C)Graph 3

Question 45

Select the correct Answer for each question.
Use the laws of logarithms to expand the expression.

A)
B)
C)
D)

Question 46

Select the correct Answer for each question.
Find the points of intersection of the graphs of the functions.Express yourAnswers accurate to five decimal places.

A)(-0.55126, -5.84352), (3.87001, 6.53604)
B)(-0.55126, -1.54352) (0.28124, 10.83604) (3.87001, 0.78748)
C)(-0.55126, -1.54352) (3.87001, 0.78748)
D)(-0.55126, -5.84352), (0.28124, -3.51252) (3.87001, 6.53604)

Question 47

Select the correct Answer for each question.
Find the exact value of the expression.

A)7
B)8
C)6
D)4
E)5

Question 48

Select the correct Answer for each question.
What is the equation of this graph?

A)
B)
C)
D)
E)

Question 49

Select the correct Answer for each question.
Find the range of the function.

A)
B)
C)
D)
E)

Question 50

Select the correct Answer for each question.
A rectangle has perimeter m.Express the area of the rectangle as a function of the length of one of its sides.

A)
B)
C)
D)
E)

Question 51

Select the correct Answer for each question.
Which of the following graphs is neither even nor odd?

A)
B)
C)

Question 52

Select the correct Answer for each question.
The graphs of and are given.For what values of is ?

A)4, 2
B)0
C)
D)
E)-4, 12

Question 53

Select the correct Answer for each question.
Starting with the graph of , find the equation of the graph that results from reflecting about the line

A)
B)
C)
D)
E)

Question 54

Select the correct Answer for each question.
Find a formula for the inverse of the function.

A)
B)
C)
D)
E)

Question 55

Select the correct Answer for each question.
Find the domain.

A)
B)
C)
D)
E)

Question 56

Select the correct Answer for each question.
The relationship between the Fahrenheit and Celsius temperature scales is given by the linear function. What is the F-intercept and what does it represent?

A) Fahrenheit temperature corresponding to
B) Celsius temperature corresponding to
C) Celsius temperature corresponding to
D) Fahrenheit temperature corresponding to
E) Fahrenheit temperature corresponding to

Question 57

Select the correct Answer for each question.
The graph of the function follows.Choose the graph of

A)
B)
C)
D)

Question 58

Select the correct Answer for each question.
Starting with the graph of write the equation of the graph that results from shifting 5 units right.

A)
B)
C)
D)
E)

Question 59

Select the correct Answer for each question.
Suppose that the graph of is drawn on a coordinate grid where the unit of measurement is an inch.How many miles to the right of the origin do we have to move before the height of the curve reaches 2 ft? Rounded to the nearest mile.

A)754.9 mi
B)4,457,536.9 mi
C)53,490,543 mi
D)53,490,442.5 mi
E)53,490,343 mi

Question 60

Select the correct Answer for each question.
If and find a function g such that

A)
B)
C)
D)
E)

Question 61

Select the correct Answer for each question.
A rectangle has perimeter m.Express the area of the rectangle as a function of the length of one of its sides.

A)
B)
C)
D)
E)

Question 62

Select the correct Answer for each question.
The graph of the function has been compressed horizontally by a factor of 2.Find the function for the transformed graph.

A)
B)
C)
D)

Question 63

Select the correct Answer for each question.
A box with an open top is to be constructed from a rectangular piece of card board with dimensions in.by in.by cutting out equal squares of side at each corner and then folding up the sides as in the figure.Express the volume of the box as a function of

A)
B)
C)
D)
E)

Question 64

Select the correct Answer for each question.
Use the Law of Exponents to rewrite and simplify the expression.

A)
B)
C)
D)
E)

Question 65

Select the correct Answer for each question.
Find the exact value of the given expression.

A)
B)0
C)
D)1

Question 66

Select the correct Answer for each question.
The relationship between the Fahrenheit and Celsius temperature scales is given by the linear function. What is the F-intercept and what does it represent?

A) Fahrenheit temperature corresponding to
B) Celsius temperature corresponding to
C)32, Celsius temperature corresponding to
D)0, Fahrenheit temperature corresponding to
E)32, Fahrenheit temperature corresponding to

Question 67

Select the correct Answer for each question.
Find the inverse of Then sketch the graphs of and on the same set of axes.

A)
B)
C)
D)

Question 68

Select the correct Answer for each question.
Find all solutions of the equation correct to two decimal places.

A)
B)
C)
D)
E)

Question 69

Select the correct Answer for each question.
What is the equation of this graph?

A)
B)
C)
D)
E)

Question 70

Select the correct Answer for each question.
Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations.

A)
B)
C)
D)

Question 71

Select the correct Answer for each question.
Find the inverse function of

A)
B)
C)
D)
E)

Question 72

Select the correct Answer for each question.
If find and simplify where

A)
B)
C)
D)

Question 73

Select the correct Answer for each question.
The graph of the function is given.State the value of .

A)
B)
C)
D)
E)

Question 74

Select the correct Answer for each question.
Find the domain and sketch the graph of the function.What is its range?

A)
B)
C)
D) x

Question 75

Select the correct Answer for each question.
Suppose that the graph of is given is given.Describe how the graph of the function can be obtained from the graph of

A)Shift the graph 3 units to the right and 3 units down.
B)Shift the graph 3 units to the right and 3 units up.
C)Shift the graph 3 units to the left and 3 units down.
D)Shift the graph 3 units to the left and 3 units up.
E)None of these

Question 76

Select the correct Answer for each question.
Starting with the graph of write the equation of the graph that results from shifting 3 units right.

A)
B)
C)
D)
E)

Question 77

Select the correct Answer for each question.
Simplify the expression.

A)12
B)36
C)8
D)64

Question 78

Select the correct Answer for each question.
Find the function and its domain if and .

A)
B)
C)
D)

Question 79

Select the correct Answer for each question.
Which of the following graphs is the graph of the function?

A)Graph 3
B)Graph 1
C)Graph 2

Question 80

Select the correct Answer for each question.
Find for the function nd the real number

A)2
B)1
C)3
D)0