Deck 10: Inverse, Exponential, and Logarithmic Functions

Question 1

Determine whether or not the function is one-to-one.

- $\{(19,-5),(14,1),(1,10)\}$

Answer 1

True

Question 2

Determine whether or not the function is one-to-one.

- $\{(-8,-18),(-17,-18),(-10,-4)\}$

Answer 2

False

Question 3

Determine whether or not the function is one-to-one.

- $\{(6,6),(7,6),(8,4),(9,-6)\}$

Answer 3

False

Question 4

Determine whether or not the function is one-to-one.

-This chart shows the number of hits for five Little League baseball teams.

Question 5

Determine whether or not the function is one-to-one.

-This chart shows the number of living relatives in five families.

Question 6

Determine whether or not the function is one-to-one.

-The function that pairs the temperature in degrees Fahrenheit of a cup of coffee with its temperature in degrees Celsius.

Question 7

Determine whether or not the function is one-to-one.

-The function that pairs the radius of a spherical bowling ball with its volume.

Question 8

Determine whether or not the function is one-to-one.

- $f(x)=2 x-4$

Question 9

Determine whether or not the function is one-to-one.

- $f(x)=x^{2}-5$

Question 10

Determine whether or not the function is one-to-one.

- $f(x)=3 x^{2}-5$

Question 11

Determine whether or not the function is one-to-one.

- $f(x)=x^{3}-1$

Question 12

Determine whether or not the function is one-to-one.

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

Question 13

Determine whether or not the function is one-to-one.

-

Question 14

Determine whether or not the function is one-to-one.

-

Question 15

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."

- $\{(9,-5),(13,6),(19,20)\}$

A) $\{(9,6),(9,13),(20,19)\}$
B) $\{(-5,9),(19,13),(20,6)\}$
C) $\{(-5,9),(6,13),(20,19)\}$
D) Not one-to-one

Question 16

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."

- $\{(-6,8),(-19,8),(-7,-12)\}$

A) $\{(-6,8),(8,-19),(-12,-7)\}$
B) $\{(8,-6),(-7,-19),(-12,8)\}$
C) Not one-to-one
D) $\{(8,-6),(8,-19),(-12,-7)\}$

Question 17

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."

- $\{(-2,4),(2,-4),(8,-2),(-8,2)\}$

A) $\{(4,-2),(-4,2),(-2,8),(2,-8)\}$
B) $\{(4,-2),(-4,2),(-2,-8),(2,8)\}$
C) Not one-to-one
D) $\{(4,-2),(-4,2),(8,-2),(2,-8)\}$

Question 18

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."

- $\left\{\left(-3, \frac{1}{2}\right),(-2,-3),\left(-\frac{1}{3}, 2\right),\left(-9, \frac{3}{8}\right)\right\}$

A) $\left\{\left(\frac{1}{2}, 3\right),(-3,2),\left(2, \frac{1}{3}\right),\left(-\frac{3}{8},-9\right)\right\}$
B) $\left\{\left(\frac{1}{3},-3\right),(-3,-2),\left(2,-\frac{1}{2}\right),\left(\frac{3}{8},-9\right)\right\}$
C) Not one-to-one
D) $\left\{\left(\frac{1}{2},-3\right),(-3,-2),\left(2,-\frac{1}{3}\right),\left(\frac{3}{8},-9\right)\right\}$

Question 19

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."

- $f(x)=8 x^{2}-4$

A) Not one-to-one
B) $f^{-1}(x)=\sqrt{\frac{x+4}{8}}$
C) $f^{-1}(x)=\frac{x+4}{8}$
D) $f^{-1}(x)= \pm \sqrt{\frac{x+4}{8}}$

Question 20

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."

- $f(x)=x^{3}-5$

A) Not one-to-one
B) $f^{-1}(x)=x+5$
C) $f^{-1}(x)= \pm \sqrt[3]{x+5}$
D) $f^{-1}(x)=\sqrt[3]{x+5}$

Question 21

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."

- $f(x)=4 x-6$

A) $f^{-1}(x)=\frac{x-6}{4}$
B) $f^{-1}(x)=\frac{x}{4}+6$
C) Not one-to-one
D) $f^{-1}(x)=\frac{x+6}{4}$

Question 22

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."

- $f(x)=3 x^{3}-6$

A) $f^{-1}(x)=\sqrt[3]{\frac{x+6}{3}}$
B) Not one-to-one
C) $f^{-1}(x)=\sqrt[3]{\frac{x-6}{3}}$
D) $f^{-1}(x)=\sqrt[3]{\frac{x}{3}}+6$

Question 23

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."

- $f(x)=\frac{8}{x-9}$

A) $f^{-1}(x)=\frac{-9+8 x}{x}$
B) Not one-to-one
C) $f^{-1}(x)=\frac{9 x+8}{x}$
D) $f^{-1}(x)=\frac{x}{-9+8 x}$

Question 24

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."

- $f(x)=\sqrt{x+9}$

A) $f^{-1}(x)=x^{2}-9, x \geq 0$
B) $f^{-1}(x)=\sqrt{x-9}$
C) Not one-to-one
D) $f^{-1}(x)=(x+9)^{2}$

Question 25

Find the indicated value.

-Let $f(x)=3^{x} \cdot f(4)$

A) 27
B) 81
C) 243
D) 12

Question 26

Find the indicated value.

-Let $f(x)=2^{x} \cdot f(-3)$

A) -8
B) $\frac{1}{6}$
C) $\frac{1}{4}$
D) $\frac{1}{8}$

Question 27

Find the indicated value.

-Let $f(x)=2^{x} \cdot f^{-1}(8)$

A) $\frac{1}{2}$
B) $\frac{3}{2}$
C) 2
D) 3

Question 28

Find the indicated value.

-Let $f(x)=2^{x} \cdot f^{-1}\left(\frac{1}{16}\right)$

A) -2
B) -4
C) 4
D) $-\frac{1}{16}$

Question 29

Use the horizontal line test to determine if the function is one-to-one.

-

Question 30

Use the horizontal line test to determine if the function is one-to-one.

-

Question 31

Use the horizontal line test to determine if the function is one-to-one.

-

Question 32

Use the horizontal line test to determine if the function is one-to-one.

-

Question 33

Use the horizontal line test to determine if the function is one-to-one.

-

Question 34

Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes.

- $f(x)=3 x$

A)


B)


C)

D)

Question 35

Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes.

- $f(x)=\sqrt{x+2}$

A)


B)


C)


D)

Question 36

Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes.

- $f(x)=x^{3}+5$

A)


B)


C)


D)

Question 37

Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes.

- $f(x)=-4 x$

A)

B)
C)
D)

Question 38

Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes.

- $f(x)=-5 x+4$

A)

B)

C)

D)

Question 39

Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes.

- $f(x)=-\sqrt{x+3}$

A)

B)

C)

D)

Question 40

Graph the function.

- $f(x)=5 x$

A)

B)

C)

D)

Question 41

Graph the function.

- $f(x)=\left(\frac{1}{4}\right)^{x}$

A)

B)

C)

D)

Question 42

Graph the function.

- $f(x)=4-x$

A)

B)

C)

D)

Question 43

Graph the function.

- $f(x)=24 x-2$

A)

B)

C)

D)

Question 44

Graph the function.

- $f(x)=4 x-2$

A)

B)

C)

D)

Question 45

Solve the equation.

- $4^{X}=16$

A) $\{2\}$
B) $\{4\}$
C) $\{1\}$
D) $\{3\}$

Question 46

Solve the equation.

- $2-x=\frac{1}{16}$

A) $\{-4\}$
B) $\left\{\frac{1}{8}\right\}$
C) $\left\{\frac{1}{4}\right\}$
D) $\{4$

Question 47

Solve the equation.

- $3(10-2 x)=81$

A) $\{5\}$
B) $\{27\}$
C) $\{-3\}$
D) $\{3\}$

Question 48

Solve the equation.

- $4^{(1+2 \mathrm{x})}=1024$

A) $\{8\}$
B) $\{-2\}$
C) $\{2\}$
D) $\{256\}$

Question 49

Solve the equation.

- $4(7-3 x)=\frac{1}{16}$

A) $\{3\}$
B) $\{-3\}$
C) $\left\{\frac{1}{4}\right\}$
D) $\{8\}$

Question 50

Solve the equation.

- $4^{\mathrm{x}}=\frac{1}{64}$

A) $\{-3\}$
B) $\left\{\frac{1}{3}\right\}$
C) $\{3\}$
D) $\left\{\frac{1}{16}\right\}$

Question 51

Solve the equation.

- $2(7+3 x)=\frac{1}{4}$

A) $\{4\}$
B) $\{3\}$
C) $\{-3\}$
D) $\left\{\frac{1}{2}\right\}$

Question 52

Solve the equation.

- $\left(\frac{2}{5}\right)^{x}=\frac{125}{8}$

A) $\left\{\frac{1}{3}\right\}$
B) \{3\}
C) $\{-3\}$
D) $\left\{-\frac{1}{3}\right\}$

Question 53

Solve the equation.

- $27^{x}=81(3 x-1)$

A) $\frac{1}{2}$
B) $-\frac{4}{9}$
C) $\frac{1}{9}$
D) $\frac{4}{9}$

Question 54

Using the exponential key of a calculator to find an approximation to the nearest thousandth.

- $17^{2.2}$

A) $662,499.529$
B) 509.316
C) 289
D) 37.4

Question 55

Using the exponential key of a calculator to find an approximation to the nearest thousandth.

- $0.4^{3.725}$

A) 192.533
B) 0.033
C) 1.49
D) 1.6

Question 56

Using the exponential key of a calculator to find an approximation to the nearest thousandth.

-2.5973 .8

A) 9.869
B) 32.04
C) 6.744
D) 37.583

Question 57

Using the exponential key of a calculator to find an approximation to the nearest thousandth.

- $2.568^{-3.8}$

A) -30.824
B) 0.152
C) 0.028
D) 0.102

Question 58

An accountant tabulated a firm's profits for four recent years in the following table:
The accountant then fit both a linear graph and an exponential curve (seen below) to the data, in order to estimate future profits. Use the linear graph to estimate the profits in the year 2001.

A) About $\$ 700,000$
B) About $\$ 800,000$
C) About $\$ 500,000$
D) About $\$ 900,000$

Question 59

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

The accountant then fit both a linear graph and an exponential curve (seen below) to the data, in order to estimate future profits. Use the exponential graph to estimate the profits in the year 2002.

A) About $\$ 1,000,000$
B) About $\$ 750,000$
C) About \$1,300,000
D) About $\$ 1,700,000$

Question 60

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

The accountant then fit both a linear graph and an exponential curve (seen below) to the data, in order to estimate future profits. Use the linear graph to estimate the profits in the year 2002.

A) About $\$ 900,000$
B) About $\$ 500,000$
C) About \$1,000,000
D) About $\$ 800,000$

Question 61

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

The accountant then fit both a linear graph and an exponential curve (seen below) to the data, in order to estimate future profits. Use the exponential graph to estimate the profits in the year 2001.

A) About \$1,000,000
B) About $\$ 750,000$
C) About \$1,300,000
D) About $\$ 300,000$

Question 62

A computer is purchased for $\$ 3200$ . Its value each year is about $77 \%$ of the value the preceding year. Its value, in dollars, after $t$ years is given by the exponential function $V(t)=3200(0.77)^{t}$ . Find the value of the computer after 4 years.

A) $\$ 9856.00$
B) $\$ 866.17$
C) $\$ 1124.90$
D) $\$ 666.95$

Question 63

A city is growing at the rate of $0.5 \%$ annually. If there were $3,889,000$ residents in the city in 1994 , find how many (to the nearest ten-thousand) were living in that city in 2000. Use $\mathrm{y}=3,889,000(2.7)^{0.005 t}$

A) $4,040,000$
B) $10,500,000$
C) $4,010,000$
D) 320,000

Question 64

The amount of particulate matter left in solution during a filtering process decreases by the equation $P=200(0.5)^{0.4 n}$ , where $\mathrm{n}$ is the number of filtering steps. Find the amounts left for $\mathrm{n}=0$ and $\mathrm{n}=5$ . (Round to the nearest whole number.)

A) 200,800
B) 200,6
C) 200,50
D) 400,50

Question 65

The number of dislocated electric impulses per cubic inch in a transformer increases when lightning strikes by $\mathrm{D}=6600(2)^{\mathrm{x}}$ , where $\mathrm{x}$ is the time in milliseconds of the lightning strike. Find the number of dislocated impulses at $\mathrm{x}=0$ and $\mathrm{x}=5$ .

A) 13, $200 ; 211,200$
B) $6600 ; 66,000$
C) $6600 ; 211,200$
D) $6600 ; 26,400$

Question 66

The number of bacteria growing in an incubation culture increases with time according to $B=9500(5)^{x}$ , where $x$ is time in days. Find the number of bacteria when $x=0$ and $x=2$ .

A) 47, $500 ; 237,500$
B) $9500 ; 29,687,500$
C) $9500 ; 237,500$
D) $9500 ; 95,000$

Question 67

The half-life of a certain radioactive substance is 36 years. Suppose that at time $t=0$ , there are $27 \mathrm{~g}$ of the substance. Then after $t$ years, the number of grams of the substance remaining will be $\mathrm{N}(\mathrm{t})=$ $27(1 / 2)^{t / 36}$ . How many grams of the substance will remain after 198 years?

A) $0.6 \mathrm{~g}$
B) $0.3 \mathrm{~g}$
C) $0.07 \mathrm{~g}$
D) $0.15 \mathrm{~g}$

Question 68

The number of bacteria growing in an incubation culture increases with time according to $B(x)=6700(2)^{x}$ , where $x$ is time in days. Find the number of bacteria when $x=0$ .

A) 26,800
B) 13,400
C) 40,200
D) 6700

Question 69

The number of bacteria growing in an incubation culture increases with time according to $B(x)=8800(4)^{x}$ , where $x$ is time in days. After how many days will the number of bacteria in the culture be 563,200 ?(Hint: Let $B(x)=563,200$ .)

A) 6 days
B) 10 days
C) 1 day
D) 3 days

Question 70

Why can't we call $\mathrm{y}=(-2)^{\mathrm{x}}$ an exponential function?

Question 71

Why can't $y=2^{x}$ have an $x$ -intercept?

Question 72

What are the domain and range for the equation $y=2^{x}$ ?

A) Domain: $(\infty, \infty)$ ; range: $(0, \infty)$
B) Domain: $(\infty, \infty)$ ; range: $(\infty, \infty)$
C) Domain: $(0, \infty)$ ; range: $(\infty, \infty)$
D) $(\infty, \infty)$ ; range: $[0, \infty)$

Question 73

With the exponential function $f(x)=a^{x}$ , why must $a \neq 0$ ?

Question 74

The table below gives the actual values of the population of a small island in the Pacific Ocean. The population is modeled by the equation $\mathrm{y}=75.2(1.055)^{\mathrm{x}}$ , where $\mathrm{x}=0$ represents the population of the island in 1990.


For the point displayed in the calculator screen above, how does the model compare to the actual?

A) The display indicates that for the year 1993, the model gives a value of about 87 people, which is slightly less than the actual value of 88 people.
B) The display indicates that for the year 1990, the model gives a value of 75.2 people, which is slightly more than the actual value of 75 people.
C) The display indicates that for the year 1993, the model gives a value of about 88 people, which is slightly more than the actual value of 87 people.
D) The display indicates that for the year 1995 , the model gives a value of about 88 people, which is slightly more than the actual value of 87 people.

Question 75

Evaluate the logarithm.

- $\log _{3}\left(\frac{1}{3}\right)$

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

Question 76

Evaluate the logarithm.

- $\log _{5}\left(\frac{1}{25}\right)$

A) -2
B) 5
C) 2
D) -5

Question 77

Evaluate the logarithm.

- $\log _{7}\left(\frac{1}{343}\right)$

A) 49
B) -49
C) -3
D) 3

Question 78

Evaluate the logarithm.

- $\log _{10}\left(\frac{1}{1000}\right)$

A) 3
B) -100
C) -3
D) 100

Question 79

Evaluate the logarithm.

- $\log _{10} 100$

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

Question 80

Evaluate the logarithm.

- $\log _{1 / 9} 9$

A) 2
B) -2
C) 1
D) -1