Deck 2: Functions and Their Graphs

Question 1

Suppose that f and g are the functions defined by the tables below. What is the domain of f ?

Answer 1

{1, 2, 3, 4}

Question 2

Suppose that f and g are the functions defined by the tables below. What is the domain of g?

A) {3, 4, 5, 6}
B) {5, 6, 7, 8}
C) {1, 2, 3, 7}
D) {2, 3, 4, 6}

Answer 2

{5, 6, 7, 8}

Question 3

Suppose that f and g are the functions defined by the tables below. What is the range of f ?

Answer 3

{3, 4, 5, 6}

Question 4

Suppose that f is the function defined by the table below. The number 6 is in the domain of f.

Question 5

Suppose that f and g are the functions defined by the tables below. What is the range of g?

A) {8, 9, 10, 11}
B) {9, 10, 11, 12}
C) {10, 11, 12, 13}
D) {7, 8, 9, 10}

Question 6

Suppose that f is the function defined by the table below. Give the table of values of f ^-1.

Question 7

Suppose that g is the function defined by the table below. The number 7 is in the domain of $g^{-1}$ .

Question 8

Suppose that f is the function defined by the table below. What is the domain of f ^-1?

A) {8, 9, 10, 11}
B)

C) {10, 11, 12, 13}
D) {8, 10, 12, 14}

Question 9

Suppose that g is the function defined by the table below. What is the range of g ^-1?

Question 10

If the function f is given by the following table, then $f^{ -1}$ can be represented by the adjacent graph.

Question 11

Sketch the graph of g ^-1, where g is the function defined by the table below.

A)

B)

C)

D)

Question 12

If f is defined by the first table of values, then is defined for the last table of values, regardless the value of k.

Question 13

Suppose that f and g are the functions defined by the tables below. Give the table of values of

.

Question 14

Suppose that f and g are the functions defined by the tables below. Give the table of values of

.

Question 15

Consider the function f with domain [0, 12] whose graph is shown below.

A) What is the largest interval contained in the domain of f on which f is increasing?
B) Let g denote the function obtained from f by restricting the domain to the interval in part (a). What is the domain of g ^-1 ?

Question 16

Consider the function f with domain [0, 12] whose graph is shown below.

A) What is the largest interval contained in the domain of f on which f is decreasing?
B) Let h denote the function obtained from f by restricting the domain to the interval in part (a). What is the range of h ^-1 ?

Question 17

Consider the function f with domain (0, 20] whose graph is shown below, where a = 4, b = 12, and c = 20. Find the largest interval where f is increasing.

A) (0, 4]
B) (12, 20)
C) [8, 20]
D) [12, 20]

Question 18

Consider the function f whose graph is shown below. Find the interval(s) where the function is decreasing. Here, a = -8, b = -4, c = 6, and d = 20.

Question 19

Every odd function is one-to-one.

Question 20

The sum of two decreasing functions is decreasing.

Question 21

Consider the function f whose graph is shown below. Use the horizontal line test to determine if the function has an inverse.

Question 22

Consider the function f whose graph is shown below. Sketch the graph of the inverse.

Question 23

Suppose f(x) = 9x + 1. Evaluate f ^-1(10).

Question 24

Suppose f(x) = -x - 16. Evaluate f ^-1(-11).

A) 16
B) 14
C) -5
D) 15

Question 25

Suppose . Evaluate f ^-1(2).

Question 26

Suppose
. Evaluate f ^-1(14).

Question 27

Suppose f(x) = 43x + 1. Find a formula for f ^-1.

Question 28

Suppose f(x) = 2x + 7. Find a formula for f ^-1.

Question 29

Suppose
. Evaluate f ^-1(4).

A) 4
B) 5
C) 3
D) -4

Question 30

Suppose

. Evaluate f ^-1(-11).

Question 31

Suppose h(x) = -11 + x², where the domain of h is the set of positive numbers. Find a formula for h^-1.

Question 32

Suppose h(x) = -6 - 2x², where the domain of h is the set of positive numbers. Find a formula for h^-1.

Question 33

Suppose

. Find the domain of f.

Question 34

Suppose
. Find the domain of f ^-1.

Question 35

Suppose
. Find the range of f ^-1.

Question 36

Suppose . Find the range of f.

A)

B)

C)

D)

Question 37

Suppose f(x) = x² + 20, where the domain of f equals
. Find the range of f.

Question 38

Suppose f(x) = 2 - 16x², where the domain of f equals
. Find the domain of f ^-1.

Question 39

Suppose f(x) = x⁵ + 17x³. Which of the following alternatives equals
?

A) 1
B)

C)

D)

Question 40

Suppose f(x) = 5x³ + x. Which of the following alternatives equals f ^-1(630)?

A) 5
B)

C) 6
D)

Question 41

Suppose f(x) = x⁷ + x⁵. Evaluate (f ^-1(13))⁷ + (f ^-1(13))⁵ + 13.

Question 42

Suppose f(x) = x⁷ + 2x³. Evaluate (f ^-1(12))⁷ + 2(f ^-1(12))³ + 1.

Question 43

Suppose
and . Evaluate
.

Question 44

Suppose and . Evaluate
.

Question 45

Suppose And . Then which must be true?

A)

B)

C)
D) Impossible to determine

Question 46

Suppose
and $g(x) = \sqrt{x-10}$ . Determine if f and g are inverses.

Question 47

Suppose
and $g(x) = \frac{x-3}{10}$ . Determine if f and g are inverses.

Question 48

Suppose on the domain $(-\infty, \infty)$ Determine if f has an inverse.

Question 49

Assuming that f and g are the functions completely defined by the tables below, evaluate the expression
.

Question 50

Assuming that g is the function completely defined by the table below, evaluate the expression
.

Question 51

Assuming that f and g are the functions completely defined by the tables below, evaluate the expression

.

Question 52

Assuming that f is the function completely defined by the table below, evaluate the expression .

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

Question 53

Evaluate assuming that and
.

Question 54

Evaluate assuming that and
.

Question 55

Evaluate Assuming that And
.

A)

B)

C)

D)

Question 56

Evaluate assuming that and
.

Question 57

Suppose
. If f(x) = (x + 9)², then find a function g such that
.

Question 58

Suppose
. If , then find a function g such that

.

Question 59

Suppose . If , then find a function f such that
.

A)

B)

C)

D)

Question 60

Suppose
. If , then find a function f such that

.

Question 61

Suppose
. If , then find a function f such that

.

Question 62

For And , find a formula for . Simplify your results as much as possible.

A)

B)

C)

D)

Question 63

For and , find a formula for . Simplify your results as much as possible.

Question 64

For and , find a formula for . Simplify your results as much as possible.

Question 65

if $f(x)=7\sqrt{x} and g(x)=\frac{x^2}{49}$ then f(g(x)) = g(f(x)) for each x > 0.

Question 66

Find a number b such that , where and
.

Question 67

Find a number c such that , where
And .

A) 241
B) -239
C) -209
D) -210

Question 68

If f(x) = 6x + b and g(x) = 6x + c, then f g = g 11eecfcf_3157_7930_ac77_83cb757619bc_TB10659_11f if and only if b = c.

Question 69

For and , find a formula for . Simplify your results as much as possible.

Question 70

For and , find a formula for . Simplify your results as much as possible.

Question 71

For and , find a formula for
. Simplify your results as much as possible.

Question 72

For and , find a formula for . Simplify your results as much as possible.

Question 73

For and , find a formula for . Simplify your results as much as possible.

Question 74

For and , find a formula for . Simplify your results as much as possible.

Question 75

For and , find a formula for
. Simplify your results as much as possible.

Question 76

Choose the composite of functions that would create the graph:

A)
For And
B)
For And
C)
For And
D)
For And

Question 77

Choose the composite of functions that would create the graph:

A)
For And
B)
For And
C)
For And
D)
For And

Question 78

Choose the composite of functions that would create the graph:

A)
For And
B)
For And
C)
For And
D)
For And

Question 79

Choose the composite of functions that would create the graph:

A)
For And
B)
For And
C)
For And
D)
For And

Question 80

Choose the composite of functions that would create the graph:

A)
For And
B)
For And
C)
For And
D)
For And