Free Printable Exponential Functions Review

1.

Describe the transformation that took place in f(x) = (2)^x -2

a)

Shifted up 2

b)

Shifted down 2

c)

Shifted right 2

d)

Shifted left 2

2.

Describe the transformation that took place in f(x) = (2)^x+3

a)

Shifted up 3

b)

Shifted down 3

c)

Shifted left 3

d)

Shifted right 3

3.

In the function, which value causes the function to shift? f(x) = 3(2)^x-1

a)

1

b)

2

c)

3

d)

x

4.

In the function, which value causes the function to stretch? f(x) = 3(2)^x-1

a)

1

b)

2

c)

3

d)

x

5.

Given the function f(x) = 5^x, write the new function g(x), if you were to shift right 3 and down 4?

a)

g(x) = (5)^x+3 - 4

b)

g(x) = (5)^x+3 + 4

c)

g(x) = (5)^x-3 + 4

d)

g(x) = (5)^x-3- 4

6.

Given the function f(x) = 5^x, write the new function g(x), that is stretched by a factor of 2 and shift up 3 units?

a)

g(x) = 2(5)^{x +3}

b)

g(x) = 2(5)^x + 3

c)

g(x) = (5)^2x + 3

d)

g(x) = (5)^{x - 3} + 2

7.

What transformation takes place in function, f(x) = 1/2(8)^x?

a)

Stretch

b)

Compression

c)

Shift left or right

d)

Shift up or down

8.

What value would need to be negative for the function to be reflected over the x-axis?
f(x) = a(b)^{x -h} +k

a)

a

b)

b

c)

h

d)

k

9.

What point will definitely be on the graph of the function f(x) = (b)^x?

a)

(0, 0)

b)

(0, 1)

c)

(1, 0)

d)

none of the above

10.

Solve for x in
2^x = 32

a)

16

b)

1

c)

4

d)

5

11.

Solve for x in
5^x= 1/125

a)

2

b)

-2

c)

3

d)

-3

12.

The domain for an exponential function is the interval:

a)

(0, 1)

b)

(H. A. , ∞)

c)

(-∞, H. A.)

d)

( -∞ , ∞)

13.

Given the parent function: f(x) = (4)^x write the function after a stretch by a factor of 3, shift up 5 units and shift right 7 units?

a)

f(x) = 3(4)^x+5 -7

b)

f(x) = 5(4)^x-7 +3

c)

f(x) = 3(4)^x+7 + 5

d)

f(x) = 3(4)^x-7 +5

14.

What is the output for f(4) given the exponential function f(x) = -3(2)^x+1 - 5

a)

-91

b)

-101

c)

91

d)

-29

15.

This graph shows

a)

exponential decay

b)

exponential growth

c)

linear function

d)

all of the above

16.

This graph shows

a)

exponential growth

b)

exponential decay

c)

linear function

d)

all of the above

17.

What is the base for the exponential function whose values are shown in the table?

a)

10

b)

2

c)

1

d)

1/2

18.

Which of the following are examples of exponential growth? (Select all that apply)

a)

y=2(0.5)^x

b)

The number of cells in a particular cell sample doubles in size every day.

c)

y=9(1-0.75)^x

19.

Which of the following are examples of exponential decay? (Select all that apply)

a)

f(x)= 4/7(1.18)^x

b)

A cars value depreciates by 18% per year.

c)

f(x)= 0.3(1.5)^x

20.

In an exponential function, what does the 'a' represent?

a)

SLOPE

b)

RATE OF CHANGE

c)

Y-INTERCEPT

d)

COMMON RATIO

21.

What is a, the starting term, for the function: f(x) = 300(1.16)^x?

a)

300

b)

1.16

c)

.16

d)

x

22.

Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)⁶

a)

Growth

b)

Decay

23.

Classify the model as Exponential GROWTH or DECAY.
A=10(1.01)³

a)

Growth

b)

Decay

24.

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

a)

y=5000(0.7)^x

b)

y=30(5000)^x

c)

y=5000(1.3)^x

d)

y=5000x^x

25.

The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 months?

a)

9766

b)

9006

c)

9765

d)

5433

26.

Is the following function exponential growth, exponential decay, linear, or none of the above?
p(x) = 13x - 5

a)

Exponential growth

b)

Exponential decay

c)

Linear

d)

None of the above

27.

The expression 12(1.015)^t models the population of elephants in a wildlife refuge after t years since 1975.
What does the value 1.015 represent?

a)

The number of elephants was 1,015 in 1975.

b)

The number of elephants increases by 1.5% each year.

c)

The number of elephants increases by 101.5% each year.

d)

The number of elephants is multiplied by 1.015 each year.

28.

A new savings account is opened with $400 and gains 3% every yr. What's the amount after 5 years?

a)

$415

b)

$463.71

c)

$343.49

d)

$460.12

29.

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the value after 7 years?

a)

$800

b)

$8367.70

c)

$6600

d)

$25,707.36

30.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

31.

Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)⁶

a)

Growth

b)

Decay

32.

You have inherited land that was purchased for $30,000 in 1960. The value of the land increased by approximately 5% per year. What is the approximate value of the land in the year 2011?

a)

$344,022

b)

$31,500

c)

$15,000

d)

$28,500

33.

An adult takes 400 mg of ibuprofen. Each hour, the amount of ibuprofen in the person’s system decreases by about 29%. How much ibuprofen is left after 6 hours?

a)

51 mg

b)

284 mg

c)

1843 mg

d)

116 mg

34.

Simplify the exponential expression.

a)

2x⁶y¹²

b)

2x⁵y⁷

c)

8x⁶y¹²

d)

8x⁵y⁷

35.

Simplify the exponential expression:

a)

10x^-2

b)

2x²

c)

2x¹²

d)

10x¹²

36.

Given y=3^xdetermine the y-intercept

a)

(0,1)

b)

(0,3)

37.

Is this exponential growth or decay?

a)

Growth

b)

Decay

38.

Classify the model as Exponential GROWTH or DECAY.
A=10(1.01)³

a)

Growth

b)

Decay

39.

Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)⁶

a)

Growth

b)

Decay

40.

Which function represents the table of values?

a)

f(x) = 4x

b)

f(x) = x³

c)

f(x) = 4^x

d)

f(x) = 4^x-1

41.

a)

The range is the set of all real numbers less than 0.

b)

The domain is the set of all real numbers greater than -4.

c)

The range is the set of all real numbers greater than 0.

d)

The domain is the set of all real numbers less than -4.

42.

The value of a painting is $12,000 in 1990 and increases by 8% of its value each year. Write and evaluate an expression to estimate the paintings value in 2005.

a)

1.08(12,000)^t = $36,000

b)

12,000(1.08)^t = $38, 066

c)

12,000(0.5)^t = $10,000

d)

12,000(0.92)^t= $40,000

43.

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

a)

y=6(0.14)^x

b)

y=6(1+14)^x

c)

y=6(1.14)^x

d)

y=6(0.86)^x

44.

What transformations occur to f(x)=5^x?

a)

translate right 3, up 2

b)

translate left 3, up 2

c)

translate left 3, down 2

d)

translate right 3, down 2

45.

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the exponential equation?

a)

y=8(15,000)^x

b)

y=15,000(1.08)^x

c)

y=15,000(0.92)^x

d)

y=15,000(0.08)^x

46.

Your shiny new boat cost $7650. The depreciation for your boat is 14% per year. What is the equation that models this problem for the value of the vehicle in 4 years?

a)

y= 7650(.14)⁴

b)

y= 7650(.86)⁴

c)

y= 7650(.86)³

d)

y= 7650(1.14)³

47.

5³⋅5⁴

a)

5⁷

b)

5⁻¹

c)

5¹²

d)

5

48.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

49.

(34x⁵y⁶z^-7)⁰

a)

34x⁵y⁶ / z⁷

b)

34x⁵y⁶ / x^-7

c)

0

d)

1

50.

Simplify the exponential expression:

a)

10x^-2

b)

2x²

c)

2x¹²

d)

10x¹²

51.

CHALLENGE:
3x³y * 2x⁸y⁵

a)

5x¹¹y⁶

b)

6x¹¹y⁶

c)

6x²⁴y⁵

d)

3x¹¹2y⁵

52.

7^-2

a)

49

b)

10/49

c)

-49

d)

1/49

53.

Solve 5^-2

a)

-10

b)

1/25

c)

1/(5)²

d)

-1/10

54.

a)

This function is an example of exponential growth.

b)

This function has a y-intercept at (0, 200).

c)

The growth factor for this function is 4.

d)

The range for this function is y > 0.

55.

Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?

a)

$23,219.72

b)

$136.72

c)

$51,710.94

d)

$16,710.94

56.

A population of fish starts at 8,000 and decreases by 6% per year. What is the population of fish after 10 years?

a)

14327

b)

4309

c)

839

d)

7680

57.

The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 months?

a)

9766

b)

9006

c)

9765

d)

5433

58.

Twenty years ago, Mr. Davis purchased his home for $160,000. Since then, the value of the home has increased about 5% per year. How much is the home worth today?

a)

$176,783.29

b)

$424,527.63

c)

$57,357.75

d)

$532,041,076.80

59.

The original value of a painting is $1400, and the value increases by 9% each year. Write an exponential growth function to model this situation.

a)

y=1400(1.09)^x

b)

y=1.09(1400)^x

c)

y=1400(.91)^x

d)

y=1.09^x

60.

What is the equation that best represents the graph?

a)

y=2^y

b)

y=2^x

c)

y=2^-x

d)

y=x²

61.

What is the domain and range of the function y=2^x?
Use the graph to help!

a)

Domain: −∞<x<∞
Range: y>0

b)

Domain: −∞<x<∞
Range: y>1

c)

Domain: −2<x<∞
Range: y>0

d)

Domain: −∞<x<∞
Range: y>0

62.

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

a)

Horizontal shift left one unit!

b)

Horizontal shift right one unit!

c)

Vertical shift up one unit!

d)

Vertical shift down one unit!

63.

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

64.

What is the horizontal asymptote for the graph of
f(x)=-2(3)^x+4-8 ?

a)

y=8

b)

y=-8

c)

x=-8

d)

x=-4

65.

What is the horizontal asymptote for the graph of
f(x)=13(0.5)^x-6?

a)

y=0.5

b)

y=13

c)

y=6

d)

y=0

66.

What is the range for

f(x)=5^x-6-3?

a)

$y\le3$

b)

$y\ge-3$

c)

(-∞, 3)

d)

(-∞, -3)

67.

What is the factor of the following Equation: $f\left(x\right)=235\left(0.78\right)^t$

a)

0.78

b)

1.78

c)

78%

d)

22%

68.

What is the rate of the following Equation: $f\left(x\right)=235\left(0.78\right)^t$

a)

0.78

b)

1.78

c)

22%

d)

0.22%

69.

What is the factor of the following Equation: $f\left(x\right)=3000\left(1.02\right)^t$

a)

0.02

b)

1.02

c)

2%

d)

0.2%

70.

What is the rate of the following Equation: $f\left(x\right)=3000\left(1.02\right)^t$

a)

0.02

b)

1.02

c)

2%

d)

0.2%

71.

Find the Domain and Range

a)

Domain : $-\infty<x<\infty$ Range: $y>0$

b)

Domain : $-\infty<x<\infty$ Range: $y>2$

c)

Domain : $-\infty<x<\infty$ Range: $y<2$

d)

Domain : $-\infty<x<\infty$ Range: $-\infty<y<\infty$

72.

Find the Domain and Range

a)

Domain : $-\infty<x<\infty$ Range: $y>0$

b)

Domain : $-\infty<x<\infty$ Range: $y>2$

c)

Domain : $-\infty<x<\infty$ Range: $y>-2$

d)

Domain : $-\infty<x<\infty$ Range: $-\infty<y<\infty$

73.

Find the Domain and Range

a)

Domain : $-\infty<x<\infty$ Range: $y>-8$

b)

Domain : $-\infty<x<\infty$ Range: $y>-6$

c)

Domain : $-\infty<x<\infty$ Range: $y<-6$

d)

Domain : $-\infty<x<\infty$ Range: $y>0$

74.

Find the Domain and Range

a)

Domain : $-\infty<x<\infty$ Range: $y>-8$

b)

Domain : $-\infty<x<\infty$ Range: $y>-4$

c)

Domain : $-\infty<x<\infty$ Range: $y<-4$

d)

Domain : $-\infty<x<\infty$ Range: $y>0$

75.

Simplify

a)

A

b)

B

c)

C

d)

D

76.

a)

A

b)

B

c)

C

d)

D

77.

IDENTIFY THE SIMPLEST EQUIVALENT EXPRESSION

a)

2m²n ⁶√m³n²

b)

8m⁹n²

c)

64^1/6m^15/6n^8/6

d)

2m³n² √m²n

78.

In simplest radical form,
2√50 is equivalent to

a)

5√2

b)

7√2

c)

10√2

d)

4√5

79.

Simplify:

a)

√4√12

b)

4√12

c)

4√3

d)

2√3

80.

a)

A

b)

B

c)

C

d)

D

81.

a)

A

b)

B

c)

C

d)

D

82.

Simplify:

a)

8x⁹

b)

8x³

c)

8x⁴√x

d)

8x³√x

83.

Simplify the expression:

a)

2xy∜2y²

b)

No Real Roots

c)

4x²y³ ∜2

d)

8x⁴y⁴ ∜2y²

84.

Simplify the radical...

√20a²b⁴

a)

2ab²√5

b)

4ab²√5

c)

5ab²√2

d)

2a²b²√5

85.

a)

y²z¹⁰√xy

b)

20yz√xy

c)

xy²z¹⁰√y

d)

yz⁶√xy²z²

86.

Simplify

a)

A

b)

B

c)

C

d)

D

87.

a)

x⁴y⁴√y

b)

72xy

c)

xy√y

d)

x²y³√x²

88.

a)

A

b)

B

c)

C

d)

D

89.

Simplify. Assume the variable is greater or equal to zero. $\sqrt{75g^3}$

a)

$5g\sqrt{3g}$

b)

$3g\sqrt{5g}$

c)

$75\sqrt{g^3}$

d)

$15\sqrt{3g^3}$

90.

Simplify. Assume the variable is greater or equal to zero. $\sqrt{20b^2}$

a)

$5\sqrt{b^2}$

b)

$10\sqrt{2b}$

c)

$2b\sqrt{5}$

d)

$20b$

91.

Simplify. Assume the variable is greater or equal to zero. $4\cdot\sqrt{18c^3}$

a)

$12c\sqrt{2c}$

b)

$6c\sqrt{6c}$

c)

$81\sqrt{c^2}$

d)

$2c\sqrt{16c}$

92.

Simplify. Assume the variable is greater or equal to zero. $10\sqrt{20y^9}$

a)

$200y\sqrt{5y}$

b)

$20y^4\cdot\sqrt{5y}$

c)

$30y^2\cdot\sqrt{y}$

d)

$20\cdot\sqrt{300y}$

93.

Simplify. Assume the variable is greater or equal to zero. $\sqrt{20b^9}$

a)

$2b^2\cdot\sqrt{5b}$

b)

$2b^4\cdot\sqrt{5b}$

c)

$b^9\cdot\sqrt{5b}$

d)

$2b\cdot\sqrt{b^5}$

94.

To solve 36 = 6^x, re-write 36 as what base and exponent?

a)

3⁶

b)

6³

c)

6²

d)

3¹²

95.

Solve 3³ = 3^{4x + 2}

a)

¼

b)

-¼

c)

½

d)

-½

96.

Solve: 7^-x = 49

a)

x = 1

b)

x = -1

c)

x = 2

d)

x = -2

97.

a)

A

b)

B

c)

C

d)

D

98.

a)

A

b)

B

c)

C

d)

D

99.

a)

A

b)

B

c)

C

d)

D

100.

a)

A

b)

B

c)

C

d)

D

101.

a)

A

b)

B

c)

C

d)

D

102.

a)

A

b)

B

c)

C

d)

D

103.

a)

A

b)

B

c)

C

d)

D

104.

a)

A

b)

B

c)

C

d)

D

105.

a)

A

b)

B

c)

C

d)

D

106.

a)

A

b)

B

c)

C

d)

D

107.

a)

A

b)

B

c)

C

d)

D

Exponential Functions Review

Total questions: 107

Worksheet time: 8hrs 22mins

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