Free Printable Chapter 6 Test Review

1.

[1.]

Which function has a horizontal asymptote?

a)

exponential

b)

logarithm

c)

both

d)

neither

2.

[2.]

Which function has a vertical asymptote?

a)

exponential

b)

logarithm

c)

both

d)

neither

3.

[3.]

How are exponentials and logarithms related?

a)

They're equal

b)

They're inverses

c)

They're not related

d)

They're reciprocals

4.

[4.]

Classify the following graph.

a)

Exponential Growth

b)

Exponential Decay

c)

Logarithmic

d)

Rational

5.

[5.]

What is the equation of the asymptote?

a)

x = 1

b)

y = 1

c)

x = -1

d)

y = -1

6.

[6.]

What is the domain?

a)

(-∞, ∞)

b)

(0, ∞)

c)

[1, ∞)

d)

(1, ∞)

7.

[7.]

What is the range?

a)

(-∞, ∞)

b)

(0, ∞)

c)

[1, ∞)

d)

(1, ∞)

8.

[8.]

What is the base?

a)

1

b)

5

c)

10

d)

3

9.

[9.]

Describe the transformation on

$g\left(x\right)=\log_2\left(x-3\right)$

a)

The graph has been shifted 3 units up

b)

The graph has been shifted 3 units to the right

c)

The graph has been shifted 2 units right

d)

The graph has been shifted 3 units left

10.

[10.]

Describe the transformation(s) for

$k\left(x\right)=\log_{10}\left(x-6\right)-4$ .

a)

k has been shifted 6 units right and 4 units down

b)

k has been shifted 6 units right and 4 units up

c)

k has been shifted 6 units left and 4 units down

d)

k has been shifted 6 units left and 4 units up

11.

[11.]

What is the domain and

range of the function y=2^x?

a)

Domain: $\left(-\infty,\infty\right)$

Range: $\left(0,\infty\right)$

b)

Domain: $\left(-\infty,\infty\right)$

Range: $\left(1,\infty\right)$

c)

Domain: $\left(-2,\infty\right)$

Range: $\left(0,\infty\right)$

d)

Domain: $\left(-\infty,\infty\right)$

Range: $\left(-\infty,0\right)$

12.

[12.]

What is the horizontal asymptote for the graph of

f(x)=2(3)^x ?

a)

y=2

b)

y=0

c)

y=3

d)

x=-4

13.

[13.]

Given the function $y=3\left(2\right)^x$ , fill in the blank in the table when $x=5$ .

a)

96

b)

7776

c)

30

d)

$-30$

14.

[14.]

What is the base in f(x)=2(6)^x+3-8 ?

a)

2

b)

6

c)

-3

d)

-8

15.

[15.]

Using the parent function y=3^x what would the graph of y=3^x+1 look like?

a)

Horizontal Shift to the right 1 unit

b)

Horizontal shift to the left one unit

c)

Vertical shift one unit up

d)

Vertical shift one unit down

16.

[16.]

Classify f(x)=-3(1.75)^x-4+6

a)

Exponential Growth

b)

Exponential Decay

17.

[17.]

Classify f(x)=4/5(.8)^x-9

a)

Exponential Growth

b)

Exponential Decay

18.

[18.]

Does the function represent exponential growth or decay?

$y=\frac{1}{8}\left(5\right)^x$

a)

Decay

b)

Growth

19.

[19.]

Describe the transformation on

$y=2\left(4\right)^x$ when if becomes $y=2\left(4\right)^{\left(x-5\right)}$

a)

Down 5

b)

Right 5

c)

Left 5

d)

Up 5

20.

[20.]

Describe the transformation on $y=\left(\frac{1}{3}\right)^x$ if it becomes $y=-\left(\frac{1}{3}\right)^{\left(x-7\right)}+2$

a)

Reflection over x-axis, left 7, up 2

b)

Reflection over x-axis, right 7, up 2

c)

Reflection over x-axis, right 2, down 7

d)

Reflection over y-axis, right 7, up 2

21.

[21.]

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

a)

16

b)

4

c)

-4

d)

None of these.

22.

[22.]

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $g\left(f\left(-1\right)\right)$

a)

2

b)

15

c)

7

d)

-9

23.

[23.]

Write equation in exponential form. $\log_2128=7$

a)

$7^2=128$

b)

$2^7=128$

c)

$128^2=7$

d)

$2^{128}=7$

24.

[24.]

Write equation in exponential form. $\log_864=2$

a)

$2^8=64$

b)

$64^8=2$

c)

$8^2=64$

d)

$2^{64}=8$

25.

[25.]

Write equation in exponential form. $\log_3\frac{1}{27}=-3$

a)

$-3^3=\frac{1}{27}$

b)

$\frac{1}{27}^3=-3$

c)

$\frac{1}{27}^{-3}=3$

d)

$3^{-3}=\frac{1}{27}$

26.

[26.]

Write the equation in logarithmic form. $27^{\frac{2}{3}}=9$

a)

$\log_{\frac{2}{3}}9=27$

b)

$\log_{27}\frac{2}{3}=9$

c)

$\log_{27}9=\frac{2}{3}$

d)

$\log_927=\frac{2}{3}$

27.

[27.]

Evaluate the logarithm. Type in the number only for the answer. $\log_381$

(a)

28.

[28.]

Evaluate the logarithm. Type in the number only for the answer. $\log_{100}10$

(a)

29.

[29.]

Evaluate the logarithm. Type in the number only for the answer. $\log_7\ \frac{1}{7}$

(a)

30.

[30.]

Evaluate the logarithm. Type in the number only for the answer. $\log_{18}1$

(a)

31.

[31.]

Evaluate the logarithm. Type in the number only for the answer. $\log_2\frac{1}{16}$

(a)

32.

[32.]

Evaluate the logarithm. Type in the number only for the answer. $\log1000$

(a)

33.

[33.]

Evaluate the logarithm. Type in the number only for the answer. $\log_{16}8$

(a)

34.

[34.]

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

35.

[35.]

According to exponent rules, when we raise an exponential expression to a power we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

36.

[36.]

Rewrite in exponential form:

ln(2) = x

a)

2^x= 10

b)

10² = x

c)

e^x= 2

d)

e² = x

37.

[37.]

Write the equation in logarithmic form. $e^3=x$

a)

$\ln x=3$

b)

$\ln3=x$

38.

[38.]

Write the equation in logarithmic form. $e^{\left(x-9\right)}=74$

a)

$\ln\left(x-9\right)=74$

b)

$x-9=\ln74$

39.

[39.]

The natural logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

40.

[40.]

log₅(4x-7)=log₅(x+5)

a)

3

b)

12

c)

4

d)

7

41.

[41.]

log₂(x²- 6) = log₂(2x+2)

a)

4, -2

b)

No Solution

c)

4

d)

-2

42.

[42.]

log₂(x+3)=4

a)

16

b)

13

c)

3

d)

10

43.

[43.]

Solve: $\log_7\left(28+3r\right)=\log_7\left(10r\right)$

a)

4

b)

7

c)

20

d)

28

44.

[44.]

3^{2x – 6} = 81

a)

x = log 4

b)

x = 5

c)

x = 4

d)

x = -1

45.

[45.]

7ⁿ⁺¹⁰- 8 = 6

a)

-7.374

b)

-8.643

c)

-7.360

d)

-8.853

46.

[46.]

Solve.

$-10+\log_3\left(x+3\right)=-10$

a)

-2

b)

no solution

c)

3

d)

-3

47.

[47.]

Solve for x.

$5e^{2x}=30$

a)

x = 896

b)

x = 0.968

c)

x = 0.896

d)

x = 0.696

48.

[48.]

$Solve\ for\ x.\ 4^{\left(2x-5\right)}=64^{3x}$

a)

x = -7/5

b)

x = -5/7

c)

x = 5

d)

x = -7

49.

[49.]

2⋅4^{3x – 6}– 8 = 120

a)

x = 3

b)

x = 4

c)

x = 7

d)

x = 8

50.

[50.]

log₁₆(x+3)=(1/4)

a)

-1

b)

1

c)

5

d)

7

51.

[51.]

8^3x+3 = 8⁶

a)

x=28

b)

x=3

c)

x=1

d)

x=12

52.

[52.]

To solve 8 = 2^5x+7, you would need to re-write 8 as what base?

a)

8

b)

4

c)

2

d)

Cannot be determined

53.

[53.]

Solve: 9^8-x = 27^x-3

a)

x = 5

b)

x = -5

c)

x = 1/5

d)

x = -1/5

54.

[54.]

Solve for a:

$5^{\left(a+2\right)}=\frac{1}{125}$

a)

-1

b)

-6/7

c)

-5

d)

4

55.

[59.]

What is the asymptote of y = 2^x - 3

a)

y = 0

b)

y = -3

c)

x = 0

d)

x = -3

56.

[60.]

How can you tell if

$y=A\left(B\right)^x$ ^{is a growth model?}

a)

B > 1

b)

B < 1

c)

B = 1

d)

A > 1

57.

[61.]

Which of the following is an exponential decay model?

a)

y = 3 * (1/2)^x

b)

y = 1/2 * (3)^x

c)

y = -2 * (2)^x

d)

y = -3 * (3/2)^x

58.

[64.]

According to exponent rules, when we raise the power to a power we _______ the exponents. Example: (e²)⁵

a)

add

b)

subtract

c)

multiply

d)

divide

59.

[65.]

Simplify to an equivalent expression BUT leave in exponent form:

$4^3\cdot4^5$

a)

$4^8$

b)

$16^8$

c)

$4^{15}$

d)

$16^{15}$

60.

[66.]

Simplify to an equivalent expression BUT leave in exponent form:

$\frac{6^{26}}{6^4}^{ }$

a)

$1^{22}$

b)

$1^{30}$

c)

$6^{22}$

d)

$6^{30}$

61.

[68.]

Simplify

ln e

a)

10

b)

1

c)

5

d)

3

62.

[69.]

Solve for x:

5^x = 17

a)

x = log₁₇5

b)

x = log 5 + log 17

c)

x = log₅17

d)

x = (log 5)/(log 17)

63.

[70.]

Evaluate the following logarithm:

$\log_2\sqrt[]{2}$

a)

-¹/₂

b)

-1

c)

1

d)

¹/₂

64.

[71].

Evaluate the following logarithm:

$\log_4\left(0.5\right)$

a)

-¹/₂

b)

-2

c)

2

d)

¹/₂

65.

[72.]

Find the inverse of y=9^x

a)

y=log_x9

b)

y=log₁₀9

c)

x=log_y9

d)

y=log₉x

66.

[73.]

Find the inverse of $y=\ln\left(x+3\right)$

a)

$y=e^x-3$

b)

$y=e^{x-3}$

c)

$y=e^x+3$

d)

$y=e^{x+3}$

67.

[75.]

Kennedy won $3,000 from a radio contest. If she puts this money in a bank account that earns 2.9% interest compounded quarterly, how much total will she earn in 10 years?

a)

$4915.59

b)

$3933.28

c)

$2979.81

d)

$4005.09

68.

[76.]

Riley invested $1,000 in savings bonds. If the bonds earn 6.75% interest compounded semi-annually, how much total will Riley earn in 15 years?

a)

$1,584.62

b)

$2,651.39

c)

$2,706.86

d)

$1,825.10

69.

[77.]

25% as a decimal:

a)

0.25

b)

02.5

c)

25

d)

2500

70.

[78.]

2% as a decimal:

a)

0.02

b)

0.2

c)

2

d)

20

71.

[79.]

What does the r stand for in this formula?

a)

Initial amount

b)

Final amount

c)

Rate

d)

Time

e)

The number of times compounded per year

72.

[80.]

What does the P stand for in this formula?

a)

Initial amount

b)

Final amount

c)

Rate

d)

Time

e)

The number of times compounded per year

73.

Evaluate log₉(9)

a)

-1

b)

1

c)

0

d)

9

74.

Simplify log₄4^3x

a)

3x

b)

3

c)

4

d)

4^3x

75.

A flea medicine breaks down at a rate of 20% per hour. This is the rate of decay of the medicine. The initial dose is 60 milligrams. Which of the following represent the equation the models the amount of flea medicine left in an animal?

a)

$y=60\left(.2\right)^x$

b)

$y=20\left(60\right)^x$

c)

$y=60\left(.8\right)^x$

d)

$y=60\left(1.2\right)^x$

76.

Select all the equations that represent exponential decay.

a)

$y=\frac{1}{2}\left(4\right)^x$

b)

$y=4\left(\frac{1}{2}\right)^x$

c)

$y=80\left(1.4\right)^x$

d)

$y=60\left(0.7\right)^x$

e)

$y=3\left(0.6\right)^x$

77.

Which equation is the inverse of the equation above?

a)

b)

c)

d)

78.

Evaluate: $5^{\log_525}$

a)

25

b)

2

c)

$\sqrt{5}$

d)

10

79.

Evaluate: $e^{\ln8}$

a)

3

b)

e

c)

8

d)

$e^8$

80.

Simplify the following: $e^5\cdot e^7$

a)

$e^{12}$

b)

$e^2$

c)

$e^7$

d)

$e^{-2}$

81.

Match the following:

a)

$\ln\left(e\right)$

1.

1

b)

$e^3$

2.

~ 20.086

c)

$\ln\left(e^3\right)$

3.

3

d)

$e^1$

4.

~ 2.718

e)

$e^{\ln\left(5\right)}$

5.

5

82.

True/False: $\log_e\ x=\ln x$

a)

True

b)

False

83.

How are exponentials and logarithms related?

a)

They're cousins

b)

They're inverses

c)

They're not related

d)

They're reciprocals

Chapter 6 Test Review

Total questions: 83

Worksheet time: 3hrs 57mins

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