Free Printable Unit 2 – Exponentials and Logarithms

1.

Stand and Fight!

a)

Yes

b)

No

2.

Given f(x) = 2x and
g(x) = x²+3 , find f(g(x)).

a)

x²+2x+3

b)

4x²+3

c)

2x²+3

d)

2x²+6

3.

Given f(x)= -3x+7 and g(x)=2x² - 8, find f(g(x)).

a)

f(g(x))= -6x²+31

b)

f(g(x))= -6x²+24

c)

f(g(x))=18x²-84x+6

d)

f(g(x))=9x²-42x-1

4.

Given f(x)= -3x + 7 and g(x)=2x² - 8, find g(f(x)).

a)

g(f(x))= -6x²+ 31

b)

g(f(x))= -6x²+ 24

c)

g(f(x))=18x²- 84x + 90

d)

g(f(x))=9x²- 42x - 41

5.

f(x) = 3x + 10
g(x) = x - 2
Find g(f(-10))

a)

-42

b)

-26

c)

-18

d)

None of these.

6.

If h(a) = 3 - 2a
Find h(-3).

a)

12

b)

-2

c)

-3

d)

9

7.

Which one is the same as fοg(x)

a)

g(f(x))

b)

f(g(x))

8.

f(x) = 3x + 10
g(x) = x - 2
Find (f∘g)(0)

a)

16

b)

4

c)

-4

d)

None of these.

9.

f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f - g)(x).

a)

x² + 8x + 1

b)

x² + 6x - 1

c)

5x² + 8x - 1

d)

x² + 8x -1

10.

a)

136

b)

4

c)

8

d)

147

11.

a)

2

b)

11

c)

-11

d)

-9

12.

Find $g\left(f\left(2\right)\right)$

a)

-4

b)

-2

c)

0

d)

4

13.

Find $f\left(g\left(4\right)\right)$

a)

1

b)

-2

c)

-3

d)

-4

14.

Find $f\left(g\left(-1\right)\right)$

(a)

15.

Find $g\left(f\left(6\right)\right)$

(a)

16.

Find $f\left(g\left(-1\right)\right)$

a)

-7

b)

-4

c)

0

d)

2

17.

Find $g\left(f\left(1\right)\right)$

a)

-7

b)

-1

c)

0

d)

2

18.

Find $g\left(f\left(-1\right)\right)$

(a)

19.

Find $f\left(g\left(-2\right)\right)$

(a)

20.

Find $g\left(f\left(0\right)\right)$

(a)

21.

Find $f\left(g\left(-2\right)\right)$

(a)

22.

Which one is the same as fοg(x)

a)

g(f(x))

b)

f(g(x))

23.

Given f(x) = 3x + 10
and g(x) = x - 2
Find f(g(5))

a)

19

b)

23

c)

-10

d)

None of these.

24.

f(x) = 3x + 10
g(x) = x - 2
Find (f∘g)(0)

a)

16

b)

4

c)

-4

d)

None of these.

25.

f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f - g)(x).

a)

x² + 8x + 1

b)

x² + 6x - 1

c)

5x² + 8x - 1

d)

x² + 8x -1

26.

If f(x) = x² and g(x) = 3x - 1, find f(g(x))

a)

9x² - 6x + 1

b)

3x - 1

c)

3x² - 1

d)

9x² - 1

27.

Find the domain and range of the $f\left(x\right)=\left(x-2\right)^2-2$ .

a)

$D_f=\left(-\infty,\infty\right),\ R_f=\left[-2,\ \infty\right)$

b)

$D_f=\left(-\infty,\infty\right),\ R_f=\left[2,\ \infty\right)$

c)

$D_f=\left(-\infty,\infty\right),\ R_f=\left(2,\ \infty\right)$

d)

$D_f=\left(-\infty,\infty\right),\ R_f=\left(-2,\ \infty\right)$

28.

Find the domain and range of the $f\left(x\right)=\sqrt{x-1}+2$ .

a)

$D_f=\left(1,\infty\right),\ R_f=\left(2,\ \infty\right)$

b)

$D_f=\left[1,\infty\right),\ R_f=\left[2,\ \infty\right)$

c)

$D_f=\left(1,\infty\right),\ R_f=\left[2,\ \infty\right)$

d)

$D_f=\left[1,\infty\right),\ R_f=\left(2,\ \infty\right)$

29.

For the functions $f\left(x\right)=1-x$ and $g\left(x\right)=1-x^2$ , find $gf\left(x\right)$ .

a)

$gf\left(x\right)=2x-x^2$

b)

$gf\left(x\right)=2x+x^2$

c)

$gf\left(x\right)=-2x-x^2$

d)

$gf\left(x\right)=-2x+x^2$

30.

Questions 18-20 are all referring to the same problem.

Consider the function f(x) = $\sqrt{x\ +\ 5}$

What is the domain and range of the function?

a)

Domain: all real numbers, Range: y $\ge$ 0

b)

Domain: x $\ge$ 5, Range: all real numbers

c)

Domain: x $\ge$ -5, Range: y $\ge$ 0

d)

Domain: x $\ge$ -5, Range: all real numbers

31.

If f(x) = 1/x and g(x) = x - 10, what is the domain of f(g(x))?

a)

{x | x not equal to 0}

b)

{x | x not equal to -10}

c)

{x | x not equal to 10}

d)

{x | x is all real numbers}

32.

Find $g\left(f\left(6\right)\right)$

(a)

33.

Compose the Function and Determine the Domain

a)

(-inf, 0) U (0, inf)

b)

(-inf, -1/2) U (-1/2, 3/2) U (3/2, inf)

c)

(-inf, 1/2) U (1/2, 3/2) U (3/2, inf)

d)

(-inf, -3/2) U (-3/2, 1/2) U (1/2, inf)

34.

Given g(x)= -3x and f(x)=x²+2, find g(f(x)).

a)

g(f(x))= -3x²-6

b)

g(f(x))= -3x²+2

c)

g(f(x))=9x²+2

d)

g(f(x))= -9x²+2

35.

a)

A

b)

B

c)

C

d)

D

36.

a)

A

b)

B

c)

C

d)

D

37.

a)

A

b)

B

c)

C

d)

D

38.

a)

A

b)

B

c)

C

d)

D

39.

a)

A

b)

B

c)

C

d)

D

40.

a)

A

b)

B

c)

C

d)

D

41.

a)

A

b)

B

c)

C

d)

D

42.

a)

A

b)

B

c)

C

d)

D

43.

a)

A

b)

B

c)

C

d)

D

44.

a)

A

b)

B

c)

C

d)

D

45.

a)

A

b)

B

c)

C

d)

D

46.

a)

A

b)

B

c)

C

d)

D

47.

a)

A

b)

B

c)

C

d)

D

48.

a)

A

b)

B

c)

C

d)

D

49.

Find the Inverse.

a)

A

b)

B

c)

C

d)

D

50.

Find the inverse.

a)

A

b)

B

c)

C

d)

D

51.

Find the inverse.

a)

A

b)

B

c)

C

d)

D

52.

Find the inverse.

a)

A

b)

B

c)

C

d)

D

53.

Find the inverse.

a)

A

b)

B

c)

C

d)

D

54.

Find the inverse.

a)

A

b)

B

c)

C

d)

D

55.

Find the domain of this composite function

f(x) = ( x - 5 ) / ( x + 1 ) g(x) = $\frac{\left(x+2\right)}{\left(x-3\right)}$

$f\degree g$

a)

X cant be 1/2

b)

X cant be 3

c)

All Real Numbers

d)

X can't be - 1/2

e)

X can't be -3

56.

Find the domain

f(x) = (x - 5)/(x+1), g(x) = (x + 2)/(x - 3)

$g\degree f$

a)

x cant be -4

b)

all real numbers

c)

x can't be 4

d)

x can't be -2

e)

x can't be -1

57.

Find the domain

f(x) = (x - 5)/(x+1), g(x) = (x + 2)/(x - 3)

f(f(x))

a)

x cant be -1

b)

x cant be 2

c)

x cant be -2

d)

all real numbers

58.

Find the domain

f(x) = (x - 5)/(x+1), g(x) = (x + 2)/(x - 3)

g(g(x))

a)

X cant be 11/2

b)

X cant be 3

c)

X can't be -11/2

d)

X cant be 5

e)

All real numbers

59.

Find the domain

f(x) = (x^2+1), g(x) = sqrt(x-1)

f(g(x))

a)

X cant be 1

b)

X can't be -1

c)

X is greater than or equal to 1

d)

X is greater than 1

e)

X is less than or equal to 1

60.

Find the domain

f(x) = (x^2+1), g(x) = sqrt(x-1)

g(f(x))

a)

all real numbers

b)

x cant be equal to negative one

61.

Find the domain

f(x) = (x^2+1), g(x) = sqrt(x-1)

f(f(x))

a)

all real numbers

b)

all real numbers except x = 1

62.

Find the domain

f(x) = (x^2+1), g(x) = sqrt(x-1)

f(f(x))

a)

x is greater than or equal than 2

b)

x is less than or equal to 2

63.

We are strong

a)

Of course!

b)

We got this!

c)

We got the energy!

64.

The relation in the graph is..

a)

a function but not a one-to-one function.

b)

a one-to-one function.

c)

not a function

65.

The relation in the graph is..

a)

a function but not a one-to-one function.

b)

a one-to-one function.

c)

not a function

66.

The relation in the graph is..

a)

a function but not a one-to-one function.

b)

a one-to-one function.

c)

not a function

67.

The relation in the graph is..

a)

a function but not a one-to-one function.

b)

a one-to-one function.

c)

not a function

68.

The relation in the graph is..

a)

a function but not a one-to-one function.

b)

a one-to-one function.

c)

not a function

69.

Which of the following graphs illustrates a one-to-one relationship?

a)

b)

c)

d)

70.

Which of the following graphs does not represent that of a one-to-one function?

a)

b)

c)

d)

71.

In which of the following formulas is the variable y a one-to-one function of the variable x? (Hint – try generating some values either in your head or using TABLES on your calculator.)

a)

$y=x^2$

b)

$y=\left|x\right|$

c)

$y=2x$

d)

$y=5$

72.

Which of the following tables illustrates a relationship in which y is a one-to-one function of x?

a)

b)

c)

d)

73.

A recent newspaper gave temperature data for various days of the week in table format. In which of the tables below is the reported temperature a one-to-one function of the day of the week?

a)

b)

c)

d)

74.

Verify if the two functions are inverses of each other. $f\left(x\right)=-x-5$

$g\left(x\right)=-3x-9$

SHOW YOUR WORK

a)

Inverse Functions

b)

Not Inverse Functions

75.

$f\left(x\right)\ =\ 5x\ -\ 5$ $g\left(x\right)\ =\ \frac{1}{5}x\ +\ 1$

Use composition of functions to determine if f(x) and g(x) are inverse functions.

SHOW YOUR WORK

a)

yes

b)

no

76.

$f(x)=3x+10$

g\left(x\right)=\frac{1}{3}x-3

Find

g(f(x))

SHOW YOUR WORK

a)

$f(g(x))=1$

b)

$f(g(x))=x$

c)

$f(g(x))=0$

d)

None of these.

77.

Verify if $f\left(x\right)$ and $g\left(x\right)$ are inverses of each other.

$f\left(x\right)=4+\frac{1}{3}x$

g\left(x\right)=3x-12

SHOW YOUR WORK

a)

Inverse Functions

b)

Not Inverse Functions

78.

What operation allows us to verify if functions are inverses?

a)

Multiplying

b)

Dividing

c)

Adding

d)

Composing

79.

To prove two functions are inverses of each other, both f(g(x)) and g(f(x)) should equal...

a)

1

b)

x

c)

0

d)

y

80.

Use composition of functions to determine if f(x) and g(x) are inverse functions.

f\left(x\right)=2\sqrt{x}-3

g\left(x\right)=\left(\frac{x+3}{2}\right)^2

SHOW YOUR WORK

a)

yes

b)

no

81.

Which of the following relations is a one-to-one function?

a)

(a)

b)

(b)

c)

(c)

d)

None of these

82.

Which of the following relations is a one-to-one function?

a)

(a)

b)

(b)

c)

(c)

d)

None of these

83.

The relation in the graph is..

a)

a function, but not a one-to-one function.

b)

a one-to-one function.

c)

not a function

84.

This is HOMEWORK

Students must use ALGEBRA to show f(g(x)) = x AND g(f(x)) = x to verify the two functions are inverses

If the two functions are not inverse only one composition must be that does not equal x

a)

I understand and will write the problems on paper and use ALGEBRA.

b)

I plan to not earn credit for this homework and will not be writing anything down on paper.

85.

Verify if the functions are inverses.

Must show ALGEBRA to verify YES or NO

a)

Inverse Functions

b)

Not Inverse Functions

86.

Verify if the functions are inverses.

Must show ALGEBRA to verify YES or NO

a)

Inverse Functions

b)

Not Inverse Functions

87.

Verify if the functions are inverses.

Must show ALGEBRA to verify YES or NO

a)

True

b)

False

88.

Verify if the functions are inverses.

Must show ALGEBRA to verify YES or NO

a)

Yes

b)

No

89.

Are f(x) =x+6 and g(x) =x-6 inverses?

Must show ALGEBRA to verify YES or NO

a)

Yes

b)

No

90.

$f\left(x\right)\ =\ 5x\ -\ 5$ $g\left(x\right)\ =\ \frac{1}{5}x\ +\ 1$

Use composition of functions to determine if f(x) and g(x) are inverse functions.

Must show ALGEBRA to verify YES or NO

a)

yes

b)

no

91.

Suppose you are given a table of values. When creating a table for the inverse graph you must...?

a)

Switch the x and y

b)

Solve for x

c)

Plot the coordinates

d)

Potato

92.

What is the inverse of the points
(1,3), (2,4), (6,8)

a)

(3,1), (4,2) and (8,6)

b)

(-3,-1), (-4,-2) and (-8,-6)

c)

(1,2), (3,4) and (6,8)

d)

(-1,-3), (-2,-4) and (-6,-8)

93.

Find the inverse of $f\left(x\right)=3x+2$

a)

$f^{-1}\left(x\right)=\frac{x-2}{3}$

b)

$f^{-1}\left(x\right)=\frac{x-3}{2}$

c)

$f^{-1}\left(x\right)=\frac{3x}{2}$

d)

$f^{-1}\left(x\right)=\frac{2+x}{3}$

94.

Find the inverse of $f\left(x\right)=-5x-7$

a)

$f^{-1}\left(x\right)=\frac{5x+7}{-7}$

b)

$f^{-1}\left(x\right)=\frac{x+5}{7}$

c)

$f^{-1}\left(x\right)=\frac{x+7}{-5}$

d)

$f^{-1}\left(x\right)=\frac{7}{-5+x}$

95.

Find the inverse of $f\left(x\right)=12x-3$

a)

$f^{-1}\left(x\right)=\frac{x+3}{12}$

b)

$f^{-1}\left(x\right)=\frac{x-3}{12}$

c)

$f^{-1}\left(x\right)=\frac{x+12}{3}$

d)

$f^{-1}\left(x\right)=\frac{x-12}{3}$

96.

Find the inverse of $f\left(x\right)=-\frac{3}{4}x+5$

a)

$f^{-1}\left(x\right)=5\left(x-\frac{4}{3}\right)$

b)

$f^{-1}\left(x\right)=-\frac{3}{4}\left(x-5\right)$

c)

$f^{-1}\left(x\right)=-\frac{4}{3}\left(x-5\right)$

d)

$f^{-1}\left(x\right)=-5\left(x-\frac{3}{4}\right)$

97.

Find the inverse of $f\left(x\right)=x^2-4$

a)

$f^{-1}\left(x\right)=\sqrt{x+16}$

b)

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

c)

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

d)

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

98.

a)

A

b)

B

c)

C

d)

D

99.

a)

A

b)

B

c)

C

d)

D

100.

Find the inverse of the equation

a)

2^(x-9)+5=y

b)

2^(x+9)-5=y

c)

5^(x-9)-5=y

101.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

102.

Which equation is the inverse of the equation above?

a)

b)

c)

d)

103.

Which equation is the inverse of the equation above?

a)

b)

c)

d)

104.

Which equation is the inverse of the equation above?

a)

b)

c)

d)

105.

Which equation is the inverse of the equation above?

a)

b)

c)

d)

106.

Find the inverse of the function:
f(x) = 10^3x

a)

f^-1(x)=log(3x)

b)

f^-1(x)=3log(x)

c)

f^-1(x)=⅓ log(x)

d)

f^-1(x)=⅓ ln(x)

107.

Find the inverse of y = 5^x- 8

a)

y=log₅(x-8)

b)

y=log₅(x+8)

c)

y=log₈(x-5)

d)

y=log₈(x+5)

108.

Find the inverse of
f(x) = 3^x-1 + 9

a)

log₃(x-9) = f^-1(x)

b)

log₃(x)-8 = f^-1(x)

c)

log₃(x-9)+1 = f^-1(x)

d)

log₃(x+9) -1 = f^-1(x)

109.

$f\left(x\right)=3x+4;\ \ g\left(x\right)=\frac{1}{3}\left(x-4\right)$

Are they inverses? Is there any solution that aren't included?

a)

Yes, its inverse

b)

No, its not inverse

c)

it results in x

d)

it does not result in x

e)

there isn't any solutions that aren't included

110.

$f\left(x\right)=\frac{\left(2x+3\right)}{x+4}\ \ \ g\left(x\right)=\frac{\left(4x-3\right)}{2-x}$

Is it an inverse and what the excluded domain values

a)

Its an inverse

b)

Its not an inverse

c)

It does not exclude any domain values

d)

It does exclude domain values

111.

Find the inverse of this function

$f\left(x\right)=\frac{\left(2x+3\right)}{\left(x+2\right)}$

(a)

112.

Rewrite log₂8 = 3 in exponential form

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

113.

Rewrite the equation into logarithmic form:
6² = 36

a)

log₆ 2 = 36

b)

log₆ 36 = 2

c)

ln 36 = 2

d)

6³⁶ = 2

114.

Write in exponential form.
log₂(¹/₈) = -3

a)

2^-3 = ¹/₈

b)

2^1/8= -3

c)

-3² = ¹/₈

d)

-3^1/8 = 2

115.

Write in logarithmic form

2^-4 = ¹/₁₆

a)

log₂(¹/₁₆) = -4

b)

log_-4(¹/₁₆) = 2

c)

log_-4 2 = ¹/₁₆

d)

log₂(-4) = ¹/₁₆

116.

To evaluate a logarithm statement log₉81, you think "9 to what power is 81".

a)

True, and it's 2

b)

False

117.

Evaluate the log by thinking " 3 to what power is 1/9" so

log₃(1/9) =

a)

1/2

b)

2

c)

-2

d)

3

118.

Evaluate by thinking 4 to what power is 16, so

log₄16

a)

2

b)

4

c)

1/2

d)

-2

119.

True or False: log₈64=2

a)

True

b)

False

120.

Evaluate log₈ 8 by thinking 8 to what power is 8, so the answer is

a)

8

b)

-1

c)

0

d)

1

121.

Evaluate log_b(b)

a)

-1

b)

0

c)

1

d)

b

122.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

123.

log₅25 = ?

a)

2

b)

5

c)

125

124.

Re-write in log form 2⁶=64

a)

log₂6=64

b)

log₂64=6

c)

log₆₄2=6

d)

log₆₄6=2

125.

Re-write in exponential form log₅625=4

a)

5⁶²⁵=4

b)

5⁴=625

c)

4⁵=625

d)

4²=16

126.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

127.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

128.

Rewrite in logarithmic form. 7⁰=1

a)

log₀7=1

b)

log₇0=1

c)

log₇1=0

d)

log₁7=0

129.

The base of common log is 10. So log 100 = ?

a)

1

b)

2

c)

10

d)

50

130.

log(4x)

a)

log4-logx

b)

log4+logx

c)

4logx

d)

xlog4

131.

log(xy²)

a)

logx+2logy

b)

logx+logy²

c)

logx-2logy

d)

logx+logy+log2

132.

$\log\left(\frac{x}{y}\right)$

a)

logx+logy

b)

xlogy

c)

log(x-y)

d)

logx-logy

133.

$\log\left(\frac{m^3}{n}\right)$

a)

logm-log3-logn

b)

3logm+logn

c)

3logm-logn

d)

3log(m-n)

134.

ln(4xy)

a)

ln4+lnx+lny

b)

4lnxy

c)

4lnx+lny

d)

4ln(x+y)

135.

log(3x)²

a)

2log(3+x)

b)

2log3+logx

c)

log3+2logx

d)

2(log3+logx)

136.

$\ln\left(\frac{2x^2y}{z^4}\right)$

a)

ln2+2lnx+lny+4lnz

b)

ln2+2lnx+lny-4lnz

c)

2ln(2xy)-4lnz

d)

2ln2x+lny-4lnz

137.

$\log\left(\frac{8x}{yz}\right)\$

a)

log8+logx-logy-logz

b)

log8+logx-logy+logz

c)

log(8x)-log(yz)

d)

8logx-ylogz

138.

log(x⁷)

a)

log(7x)

b)

log7+logx

c)

xlog7

d)

7logx

139.

$\log\left(\frac{9}{4}\right)$

a)

log9+log4

b)

log(9-4)

c)

log9-log4

d)

4log9

140.

$\log\left(\frac{m^3}{n}\right)$

a)

logm-log3-logn

b)

3logm+logn

c)

3logm-logn

d)

3log(m-n)

141.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

142.

Expand: $\log\ ab$

a)

$\log a\ -\ \log b$

b)

$b\log a$

c)

$a\log b$

d)

$\log a+\log b$

143.

Expand: $\log_b\ \frac{m}{n}$

a)

$\log_bm\ -\log_bn$

b)

$\log_bm\ +\ \log_b\ n$

c)

$m\log_bn$

d)

$n\log_bn$

144.

Expand: $\log_2\ \frac{5}{x}$

a)

$\log_25\ +\ \log_2x$

b)

$\log_2x-\log_25$

c)

$\log_25-\log_2x$

d)

$5\log_2x$

145.

Expand: $\log\ \frac{k}{d}$

a)

$k\log d$

b)

$\log k\ +\ \log\ d$

c)

$\log\ k\ -\ \log d$

d)

$\log d-\log k$

146.

Expand: $\log_7\ y^8$

a)

$\log_7y\ +\ \log_78$

b)

$\log_7y-\log_78$

c)

$8\log_7y$

d)

$\log_78+\log_7y$

147.

Expand: $\log_9\sqrt{23}$

a)

$\frac{1}{2}\log_923$

b)

$\log_9\left(\frac{1}{2}\right)-\log_923$

c)

$\log_9\sqrt{2}+\log_9\sqrt{3}$

d)

$\log_9\ \left(\frac{1}{2}\right)+\log_923$

148.

Classify the following graph.

a)

Exponential Growth

b)

Exponential Decay

c)

Logarithmic

149.

Classify the following graph.

a)

Exponential Growth

b)

Exponential Decay

c)

Logarithmic

150.

Classify the following graph.

a)

Exponential Growth

b)

Exponential Decay

c)

Logarithmic

151.

What equation matches the graph?

a)

f(x) = 3^x

b)

f(x) = (⅓)^x

c)

f(x) = log₃(x)

152.

What equation matches the graph?

a)

f(x) = 3^x

b)

f(x) = (⅓)^x

c)

f(x) = log₃(x)

153.

What equation matches the graph?

a)

f(x) = 3^x

b)

f(x) = (⅓)^x

c)

f(x) = log₃(x)

154.

Which has a horizontal asymptote?

a)

Exponential

b)

Logarithmic

c)

Both

155.

Which has a vertical asymptote?

a)

Exponential

b)

Logarithmic

c)

Both

156.

Where would the asymptote be for this graph?

a)

y = 4

b)

y = -4

c)

x = 3

d)

x = -3

157.

Where is the asymptote?

a)

x = 1

b)

y = 1

c)

x = -1

d)

y = -1

158.

What is the domain?

a)

(-∞, ∞)

b)

(0, ∞)

c)

[1, ∞)

d)

(1, ∞)

159.

What is the range?

a)

(-∞, ∞)

b)

(0, ∞)

c)

[1, ∞)

d)

(1, ∞)

160.

As x --> 1, f(x) --> ____

a)

0

b)

∞

c)

-∞

d)

1

161.

As x --> ∞, f(x) --> ____

a)

0

b)

∞

c)

-∞

d)

1

162.

a)

2^1/6

b)

64

c)

6^1/2

d)

2⁶

163.

Write the expression in radical form.

y^1/2

a)

√y

b)

∛y

c)

√y²

d)

∛y²

164.

$5^{\frac{1}{2}}$

a)

$\sqrt{5}$

b)

10

c)

25

d)

$\sqrt{25}$

165.

an exponent 1/2 means

a)

square root

b)

cube root

c)

fourth root

d)

fifth root

166.

$\sqrt{13}$

a)

$6$

b)

$13$

c)

$13^{\frac{1}{2}}$

d)

$13^2$

167.

Evaluate this expression using the quotient rule.

a)

9⁵

b)

9⁹

c)

1⁵

d)

9^-5

168.

Simplify (-1/2)⁰

a)

1

b)

0

c)

-1

d)

-2

169.

Simplify the expression x⁵x⁷

a)

x³⁵

b)

x¹²

c)

x²

d)

x^-2

170.

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

171.

a)

32t¹¹r⁸

b)

32t³⁰r¹⁵

c)

-32t³⁰r¹⁵

d)

-32t¹¹r⁸

172.

Simplify the exponential expression:

a)

10x^-2

b)

2x²

c)

2x¹²

d)

10x¹²

173.

Simplify the exponential expression.

a)

2x⁶y¹²

b)

2x⁵y⁷

c)

8x⁶y¹²

d)

8x⁵y⁷

174.

(2m⁴)(5m²)

a)

10m⁶

b)

10m⁸

c)

7m⁶

d)

7m⁸

175.

$\frac{-12x^4y^3}{3xy^2}$ Simplify:

a)

$-15xy$

b)

$-9xy$

c)

$4xy$

d)

$-4xy$

176.

Simplify: $\left(a^4b^2\right)^2\left(ab^2\right)$

a)

$a^7b^6$

b)

$a^9b^6$

c)

$a^8b^8$

d)

$\frac{1}{a^9b^6}$

177.

x⁻⁶

a)

1 ⁄ x⁶

b)

x⁶

c)

-x⁶

d)

-1 ⁄ x⁶

178.

Simplify
(2a²b⁴z)(6a³b²z⁵)

a)

8a⁵b⁶z⁶

b)

12a⁶b⁸z⁵

c)

12a⁵b⁶z⁶

d)

8a⁶b⁸z⁵

179.

$\frac{3x^3y^8}{x^5y^{14}}\cdot\frac{2x^2y^5}{x^9y^3}$

a)

$5x^9y^4$

b)

$6x^9y^4$

c)

$\frac{5}{x^9y^4}$

d)

$\frac{6}{x^9y^4}$

180.

Solve using the product law of exponents

Resolver utilizando la ley de productos de los exponentes

(5⁵)(5³)

a)

25⁸

b)

5¹⁵

c)

25¹⁵

d)

5⁸

181.

Solve using the product law of exponents.

(Espanol) Resolver utilizando la ley de productos de los exponentes.

(10¹²)(10⁴)

a)

10¹⁶

b)

10⁴⁸

c)

100¹⁶

d)

100⁴⁸

182.

Simplify.

Simplificar.

(x⁴) (x)

a)

2x⁴

b)

x

c)

x⁵

d)

x⁴

183.

Evaluate and leave answer as an exponent.

Evaluar y dejar la respuesta como exponente.

4⁸(4⁸)(4^-5)

a)

64¹¹

b)

4¹¹

c)

64²¹

d)

4^-21

184.

Use the product law to solve.

Utilice la ley de productos para resolver.

(7^-17)(7^-24)

a)

7 ^-7

b)

49⁶⁹⁷

c)

7 ^-41

d)

49 ^-41

185.

Simplify

w⁵(w^x)w⁷

a)

w^35x

b)

w¹³

c)

w^12x

d)

w^{12 + x}

186.

Solve.

Resolver.

(y⁶)(y^-11)

a)

y^-66

b)

y^-5

c)

y⁵

d)

y¹⁷

187.

Solve using the product law of exponents and simplify your answer.

Resolver utilizando la ley de productos de los exponentes y simplifica tu respuesta.

(m)(m⁶)(m^-2)

a)

m^-12

b)

m⁵

c)

m⁴

d)

m⁹

188.

Solve and leave answer as exponent.

Resolver y dejar la respuesta como exponente.

9^-13(9³)9^-1(9¹³)

a)

9²

b)

9^-2

c)

9^-30

d)

6561⁵⁰⁷

189.

Solve and leave answer as exponent.

Resolver y dejar la respuesta como exponente.

(8ⁿ)(8²)

a)

64²ⁿ

b)

8^{(2 + n)}

c)

8³

d)

8²ⁿ

190.

log(4x)

a)

log4-logx

b)

log4+logx

c)

4logx

d)

xlog4

191.

log(xy²)

a)

logx+2logy

b)

logx+logy²

c)

logx-2logy

d)

logx+logy+log2

192.

$\log\left(\frac{x}{y}\right)$

a)

logx+logy

b)

xlogy

c)

log(x-y)

d)

logx-logy

193.

$\log\left(\frac{m^3}{n}\right)$

a)

logm-log3-logn

b)

3logm+logn

c)

3logm-logn

d)

3log(m-n)

194.

Write log_b(x/y) as two logs

a)

log_bx-log_by

b)

log_bx+log_by

c)

log_bx*log_by

d)

log_bx/log_by

195.

Use multiple log properties to write as a single log:
log₂x - 5log₂y

a)

log₂(x/y⁵)

b)

log₂(xy⁵)

c)

log₂(x/y)⁵

d)

log₂(x/5y)

196.

a)

log (xy³)

b)

log (x⁶− y³)

c)

log (x⁶/y³)

d)

log (x⁶ + y³)

197.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

198.

Rewrite log_b(xⁿ)

a)

nlog_bx

b)

(log_bx)ⁿ

c)

xⁿlog_bx

d)

log_b(xⁿ)

199.

$\log\left(\frac{8x}{yz}\right)\$

a)

log8+logx-logy-logz

b)

log8+logx-logy+logz

c)

log(8x)-log(yz)

d)

8logx-ylogz

200.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

201.

When you have two log expressions separated by a minus sign (-), we really need to ___________ them to simplify into one log expression.

a)

add

b)

subtract

c)

multiply

d)

divide

202.

When you have two log expressions separated by a plus sign (+), we really need to ___________ them to simplify into one log expression.

a)

add

b)

subtract

c)

multiply

d)

divide

203.

$\log\left(\frac{4}{5}\right)$ Expand the Log

a)

$\log4\ +\log5$

b)

$\log\ 20$

c)

$\log4\ -\log5$

204.

Expand the following logarithm:
log₂ 5x.

a)

log₂ 5 - log₂ x

b)

log₂ 5 + log₂ x

c)

2log 5 + 2log x

d)

log5 2 + log_x 2

205.

a)

6log₈(xyz)

b)

log₈(x) - log₈(y) - 6log₈(z)

c)

log₈(x) + log₈(y) - log₈(z)

d)

log₈(x) + log₈(y) + 6log₈(z)

206.

a)

log(x) + log(z) + 4log(y)

b)

3log(x) − log(z) − 4log(y)

c)

3log(x) + log(z) + 4log(y)

d)

log(x) − 4log(z) − 3log(y)

207.

Write as a single log: log 12 + 2 log x

a)

log (12 + 2x)

b)

log (14x)

c)

log (12 * 2x)

d)

log (12x²)

208.

Simplify: 2log(x) + 3log(xy)

a)

log(x⁵y³)

b)

log(5xy)

c)

5log(x²y)

d)

log(6x²y)

209.

Expand

\log_5\left(\frac{12a}{2}\right)

a)

$\log_212a-\log_25$

b)

$\log_512a-\log_52$

c)

$\log_512-\log_5a-\log_52$

d)

$\log_512+\log_5a-\log_52$

210.

Using the change of base rule, what is this logarithm equivalent to?

a)

A

b)

B

c)

C

d)

D

211.

Using the change of base rule, what is this logarithm equivalent to?

a)

A

b)

B

c)

C

d)

D

212.

Using the change of base rule, what is this logarithm equivalent to?

a)

A

b)

B

c)

C

d)

D

213.

Using the change of base rule, what is this logarithm equivalent to?

a)

A

b)

B

c)

C

d)

D

214.

7^x = 36

a)

1.8416

b)

3.5835

c)

1.5563

d)

3.0903

215.

6^3x - 3 = 56

a)

2.2757

b)

1.3592

c)

0.7586

d)

0.5903

216.

Use the change of base rule to rewrite this problem:

log₅75

a)

log(75)/log(5)

b)

log(5)/log(75)

217.

Use the change of base rule to rewrite this problem:

log₆216

a)

log(6)/log(216)

b)

log(216)/log(6)

218.

Use the change of base rule to rewrite this problem:

log₇729

a)

log(7)/log(729)

b)

log(729)/log(7)

219.

Simplify the expression log₅(625)

a)

125

b)

620

c)

4

d)

5

220.

Using the change of base rule, what is this logarithm equivalent to?

a)

A

b)

B

c)

C

d)

D

221.

Using the change of base rule, what is this logarithm equivalent to?

a)

A

b)

B

c)

C

d)

D

222.

Using the change of base rule, what is this logarithm equivalent to?

a)

A

b)

B

c)

C

d)

D

223.

Using the change of base rule, what is this logarithm equivalent to?

a)

A

b)

B

c)

C

d)

D

224.

7^x = 36

a)

1.8416

b)

3.5835

c)

1.5563

d)

3.0903

225.

6^3x - 3 = 56

a)

2.2757

b)

1.3592

c)

0.7586

d)

0.5903

226.

Use the change of base rule to rewrite this problem:

log₅75

a)

log(75)/log(5)

b)

log(5)/log(75)

227.

Use the change of base rule to rewrite this problem:

log₆216

a)

log(6)/log(216)

b)

log(216)/log(6)

228.

Use the change of base rule to rewrite this problem:

log₇729

a)

log(7)/log(729)

b)

log(729)/log(7)

229.

Simplify the expression log₅(625)

a)

125

b)

620

c)

4

d)

5

230.

You want to solve for x. Which of these is the correct "step 1"?

a)

$\log_78=\log_7x$

b)

$\log_742=\log_7x$

c)

$\log_748=\log_7\left(\frac{x}{6}\right)$

d)

$\log_754=\log_7x$

231.

After step 1 is completed, we get to here. What's the same about the left and right sides of the equation? What's different?

4 lines

232.

Finish solving for x

a)

x = 6

b)

x = 7

c)

x = 8

d)

x = 56

233.

We want to solve for x. What's the first step?

a)

Rewrite as a logarithm: $\log_{189}3=x$

b)

Rewrite as a logarithm: $\log_3189=x$

c)

Rewrite 189 with a base of 3: $3^x=3^{63}$

d)

Rewrite 189 with a base of 3: $3^x=3^9$

234.

Finish solving for x.

a)

0.210 = x

b)

5 = x

c)

63 = x

d)

4.771 = x

e)

4.462 = x

235.

We want to solve for x. Which of these is the correct "step 1"?

a)

$\log\left(64\right)=\log\left(3x\right)$

b)

$\log\left(16\right)=\log\left(x^3\right)$

c)

$\log\left(16\right)=\log\left(3x\right)$

d)

$\log\left(64\right)=\log\left(x^3\right)$

e)

$\log\left(1\right)=\log\left(x^3\right)$

236.

Continue solving for x. Which is the correct "step 2"?

a)

$64=x^3$

b)

$64^3=x$

c)

$x^{64}=3$

d)

$3^{64}=x$

237.

Finish solving for x.

Fill in the blank in the box below

(a)

238.

Which is the correct "step 1" to solve for x?
Hint: look at the schoology discussions if you feel stuck

a)

$\log_2\left(100x^5\right)=7$

b)

$\log_2\left(95x\right)=7$

c)

$\log_2\left(20x\right)=7$

d)

$\log_2\left(500x\right)=7$

239.

Finish solving for x.

Hint: look at the schoology discussions if you're stuck

a)

x = 0.175

b)

x = 6.4

c)

x = 0.7

d)

x = 12.8

240.

Solve for x: $9^x=60$

a)

1.748

b)

x = 6.667

c)

x = 0.537

d)

x = 1.863

241.

Solve for x.
$\log_52+\log_5x=\log_520$
x = (a)

242.

Solve for x.
$2\log_410=\log_4\left(8x\right)+\log_4\left(5\right)$

a)

x = 2.5

b)

x = 0.5

c)

x = 1.538

d)

x = 11.875

243.

Which formula(s) should you use for compound interest?

select ALL that apply.

a)

I=\left(P\right)\left(r\right)\left(t\right)

b)

$A=P\left(1+r\right)^t$

c)

$P+I=A$

d)

$A=P\left(1+r\right)t$

244.

Ms. Pierson is working out a compound interest problem. This is what she plugged into her calculator:

500\left(1+\frac{3}{100}\right)7

Did she do that correctly?

a)

Yes, everything looks good!

b)

No, she made a mistake :(

245.

Your 3 year investment of $20,000 received 5.2% interest compounded annually. What will your total balance be at the end?

a)

$23,285.05

b)

$3,285.05

c)

$2,385

d)

$32,285

246.

The Arnold's took out a loan for $195,000 to purchase a home. At a 4.3% interest rate compounded annually, how much interest will they have paid over the course of 30 years?

a)

$494,546.99

b)

$529.305.61

c)

$689,546.99

d)

$640,891.53

247.

You borrowed $59,000 for 2 years at 11% which was compounded annually. What total will you pay back?

a)

$13,693.90

b)

$1,363.90

c)

$72,693.90

d)

$73,793.90

248.

You borrowed $1,690 for 5.5 years at an interest of 5.7% compounded annually. How much extra did you pay by taking out the loan?

a)

$602.45

b)

$2,292.45

c)

$1,87.55

d)

$3,982.45

249.

Your $440 gets 5.8% interest compounded annually for 8 years. What will your total balance be in 8 years?

Don't forget to round your answer to 2 decimal places.

(a)

250.

Jay'den earned $475 from mowing lawns last summer. He deposited this money in an account that pays an interest rate of 3.8% compounded annually.

How much interest will he end up earning over the course of 15 years?

Don't forget to round your answer to 2 decimal places.

(a)

251.

Which formula(s) should you use for compound interest?

select ALL that apply.

a)

I=\left(P\right)\left(r\right)\left(t\right)

b)

$A=P\left(1+r\right)^t$

c)

$P+I=A$

d)

$A=P\left(1+r\right)t$

252.

Ms. Pierson is working out a compound interest problem. This is what she plugged into her calculator:

500\left(1+\frac{3}{100}\right)7

Did she do that correctly?

a)

Yes, everything looks good!

b)

No, she made a mistake :(

253.

Your 3 year investment of $20,000 received 5.2% interest compounded annually. What will your total balance be at the end?

a)

$23,285.05

b)

$3,285.05

c)

$2,385

d)

$32,285

254.

The Arnold's took out a loan for $195,000 to purchase a home. At a 4.3% interest rate compounded annually, how much interest will they have paid over the course of 30 years?

a)

$494,546.99

b)

$529.305.61

c)

$689,546.99

d)

$640,891.53

255.

You borrowed $59,000 for 2 years at 11% which was compounded annually. What total will you pay back?

a)

$13,693.90

b)

$1,363.90

c)

$72,693.90

d)

$73,793.90

256.

You borrowed $1,690 for 5.5 years at an interest of 5.7% compounded annually. How much extra did you pay by taking out the loan?

a)

$602.45

b)

$2,292.45

c)

$1,87.55

d)

$3,982.45

257.

Your $440 gets 5.8% interest compounded annually for 8 years. What will your total balance be in 8 years?

Don't forget to round your answer to 2 decimal places.

(a)

258.

Jay'den earned $475 from mowing lawns last summer. He deposited this money in an account that pays an interest rate of 3.8% compounded annually.

How much interest will he end up earning over the course of 15 years?

Don't forget to round your answer to 2 decimal places.

(a)

259.

Does the function $y=4e^{0.75x}$ represent exponential growth or decay?

a)

Exponential growth of 75%

b)

Exponential decay of 75%

c)

Exponential growth of 25%

d)

Exponential decay of 25%

260.

Tritium is a chemical that decays over time. In a sample of tritium, the amount y(in millligrams) remaining after t years is given by the equation below. How much Tritium will be left after 10 years? Round to 2 decimal places. $y=10e^{-0.0562t}$

a)

4.84

b)

5.71

c)

1.32

d)

3.84

261.

Tritium is a chemical that decays over time. In a sample of tritium, the amount y(in millligrams) remaining after t years is given by the equation below. What is the half-life of Tritium? Round to 2 decimal places. $y=10e^{-0.0562t}$

a)

5.00 minutes

b)

7.87 minutes

c)

10.24 minutes

d)

12.33 minutes

262.

Miguel had 25 bacteria in his petri dish at 2 PM. There were 72 in the dish at 2:30 PM. Assuming exponential growth, at what rate are they increasing?

a)

9.6% per minute

b)

0.03526% per minute

c)

35.26% per minute

d)

3.526% per minutes

263.

The population of Guyana was roughly 787,000 in 2020 and 747,000 in 2000. If the population is growing exponentially, what is the rate of growth?

a)

0.002608

b)

0.00113

c)

0.0527

d)

.2608

264.

Which expression does NOT represent exponential decay?

a)

$5\left(0.86\right)^x$

b)

$5e^{-0.14}$

c)

$5e^{0.14x}$

d)

$5\left(0.14\right)^x$

265.

If a population of 300 animals in a certain region is growing exponential at 2% per year, when will the population reach 400?

a)

14.4 years

b)

15 years

c)

6.2 years

d)

20 years

266.

A new computer continuously loses about 45% of its value each year. If Monique spent $1600 on her computer, how much will it be worth in 5 years?

a)

$1420.00

b)

$146.31

c)

$65.61

d)

$168.64

267.

$32=64e^{r\left(23\right)}$

Using this equation above where the time is in hours, which of the following are true? Select all that apply.

a)

The half-life is 23 hours.

b)

The start amount is 64.

c)

The equation represents exponential growth.

d)

r will be a negative number.

e)

The half-life is 32 hours.

268.

Without doing any calculations, which one will increase the fastest?

a)

$100\left(1+\frac{.03}{4}\right)^{4\left(t\right)}$

b)

$100\left(1+\frac{.03}{2}\right)^{2\left(t\right)}$

c)

$100e^{.03\left(t\right)}$

d)

$100\left(1+\frac{.03}{12}\right)^{12\left(t\right)}$

Unit 2 – Exponentials and Logarithms

Total questions: 268

Worksheet time: 21hrs 16mins

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