Deck 12: Exponential Functions and Logarithmic Functions

Question 1

Solve the problem.

Answer 1

C

Question 2

Graph.

Answer 2

C

Question 3

Graph.

Answer 3

A

Question 4

Translate the sentence to an inequality.

Question 5

Solve the problem.

Question 6

Solve the problem.

Question 7

Graph.

Question 8

Solve the problem.
An accountant tabulated a firm's profits for four recent years in the following table:

Question 9

Graph.

Question 10

Graph.

Question 11

Solve the problem.
An accountant tabulated a firm's profits for four recent years in the following table:

Question 12

Solve the problem.
An accountant tabulated a firm's profits for four recent years in the following table:

Question 13

Solve the problem.

Question 14

Solve the problem.

Question 15

Graph.
f(x)= 3x

Question 16

Graph.

Question 17

Graph.

Question 18

Graph.

Question 19

Solve the problem.
Suppose that $90,000 is invested at 4% interest, compounded annually. Find a function A for the amount in the account after t years.

Question 20

Solve the problem.
An accountant tabulated a firm's profits for four recent years in the following table:

Question 21

Find the requested composition of functions.

Question 22

Translate the sentence to an inequality.

Question 23

Find f(x)and g(x)such that h(x)= (f  g)(x).
{(6, -6), (6, -5), (4, -4), (2, -3)}

A){(-6, 6), (-5, 6), (-4, 4), (-3, 2)}
B){(-5, -6), (-6, 4), (6, 6), (-5, -4)}
C){(-5, -6), (-3, 4), (6, 4), (-5, -4)}

Question 24

Find the requested composition of functions.

Question 25

Find the requested composition of functions.

Question 26

Find the requested composition of functions.

Question 27

Find the requested composition of functions.

Question 28

Find f(x)and g(x)such that h(x)= (f  g)(x).
{(10, -3), (-4, 20), (12, -20)}

A){(-3, 10), (20, -4), (-20, 12)}
B){(10, 20), (10, -4), (-20, 12)}
C){(-3, 10), (12, -4), (-20, 20)}

Question 29

Translate the sentence to an inequality.

Question 30

Find the requested composition of functions.

Question 31

Translate the sentence to an inequality.

Question 32

Find f(x)and g(x)such that h(x)= (f  g)(x).
{(-6, 2), (-2, 6), (9, -2), (-9, 2)}

A){(2, -6), (6, -2), (-2, 9), (2, -9)}
B){(2, 9), (9, -2), (2, -6), (-2, -9)}
C){(2, 9), (6, -2), (2, -2), (-2, -9)}

Question 33

Find f(x)and g(x)such that h(x)= (f  g)(x).

Question 34

Translate the sentence to an inequality.

Question 35

Find the requested composition of functions.

Question 36

Find the requested composition of functions.

Question 37

Find f(x)and g(x)such that h(x)= (f  g)(x).
{(2, 9), (-2, -9), (4, -7), (-4, 7)}

A){(9, 2), (-9, -2), (-7, -2), (7, -4)}
B){(9, 2), (2, -2), (-7, 4), (7, -4)}
C){(9, 2), (-9, -2), (-7, 4), (7, -4)}

Question 38

Translate the sentence to an inequality.

Question 39

Find the requested composition of functions.

Question 40

Translate the sentence to an inequality.

Question 41

Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line.
y = 8x - 6

Question 42

Determine whether the function is one-to-one.

- $$f ( x ) = 4 x ^ { 2 } + x$$

Question 43

Find the inverse of the relation.

Question 44

Determine whether the function is one-to-one.

- $$f ( x ) = \left| 25 - x ^ { 2 } \right|$$

Question 45

Determine whether the function is one-to-one.

- $$f ( x ) = x ^ { 2 } + 3$$

Question 46

Graph the relation using solid circles and the inverse using open circles.
{(10, -5), (8, -4), (6, -3), (4, -2)}

Question 47

Determine whether the function is one-to-one.

- $$f ( x ) = 3 x ^ { 3 } - 8$$

Question 48

Find an equation of the inverse of the relation.

Question 49

Determine whether the function is one-to-one.

- $$f ( x ) = 16 - x ^ { 2 }$$

Question 50

Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line.

Question 51

Determine whether the function is one-to-one.

-f(x)= 2x - 4

Question 52

Determine whether the function is one-to-one.

- $$f ( x ) = 7 x ^ { 2 } + 3$$

Question 53

Find an equation of the inverse of the relation.
y = 6x + 5

A)x = 5y + 6
B)y = 5x + 6
C)y = -6x - 5
D)x = 6y + 5

Question 54

Graph the relation using solid circles and the inverse using open circles.
{(2, 8), (-2, -8), (2, -6), (-2, 6)}

Question 55

Graph the relation using solid circles and the inverse using open circles.
{(-10, 14), (-17, -13), (18, 3)}

Question 56

Find an equation of the inverse of the relation.

Question 57

Graph the relation using solid circles and the inverse using open circles.
{(-8, -5), (5, 8), (9, 9), (-9, -9)}

Question 58

Determine whether the function is one-to-one.

- $$f ( x ) = x ^ { 3 } - 7$$

Question 59

Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line.
y = 6 + 5x

Question 60

Find an equation of the inverse of the relation.
y = 2 + 6x

A)y = 6 - 2x
B)x = 6 + 2y
C)y = 6 + 2x
D)x = 2 + 6y

Question 61

Use composition to verify whether or not the inverse is correct.

- $$f ( x ) = 3 x + 9 , f ^ { - 1 } ( x ) = \frac { 1 } { 3 } x - 3$$

Question 62

Use composition to verify whether or not the inverse is correct.

- $$f ( x ) = \frac { 3 } { x + 7 } , f ^ { - 1 } ( x ) = \frac { 7 x + 3 } { x }$$

Question 63

Use composition to verify whether or not the inverse is correct.

- $$f ( x ) = 6 x - 4 , f ^ { - 1 } ( x ) = \frac { x + 6 } { 4 }$$

Question 64

Determine whether the function is one-to-one.

- $$f ( x ) = \left( \frac { 1 } { 7 } \right) ^ { x }$$

Question 65

Determine whether the function is one-to-one.

Question 66

Determine whether the function is one-to-one.

Question 67

Use composition to verify whether or not the inverse is correct.

- $$f ( x ) = - \frac { 1 } { 8 } x , f ^ { - 1 } ( x ) = - 8 x$$

Question 68

Graph the function as a solid curve and its inverse as a dashed curve.

Question 69

Determine whether the function is one-to-one.

Question 70

Use composition to verify whether or not the inverse is correct.

- $$f ( x ) = x ^ { 3 } + 8 , f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x + 8 }$$

Question 71

Determine whether the given function is one-to-one. If so, find a formula for the inverse.

Question 72

Determine whether the function is one-to-one.

Question 73

Determine whether the function is one-to-one.

Question 74

Determine whether the function is one-to-one.

Question 75

Use composition to verify whether or not the inverse is correct.

- $$f ( x ) = 3 x + 6 , f ^ { - 1 } ( x ) = \frac { 1 } { 3 } x - 3$$

Question 76

Solve the problem.

Question 77

Graph the function as a solid curve and its inverse as a dashed curve.
f(x)= 5x

Question 78

Use composition to verify whether or not the inverse is correct.

- $$f ( x ) = 9 x - 9 , f ^ { - 1 } ( x ) = \frac { 1 } { 9 } x + 1$$

Question 79

Determine whether the function is one-to-one.

Question 80

Solve the problem.