Free Printable Exam Review 5/9/24

1.

Find the average rate of change over the given interval.

a)

4

b)

7

c)

7/3

d)

3/7

2.

What is the average rate of change of [1, 5]?

a)

-0.65

b)

-0.75

c)

3.75

d)

4

3.

A climber is on a hike. After 2 hours he is at an altitude of 400 feet. After 6 hours, he is at an altitude of 700 feet. What is the average rate of change?

a)

200

b)

150

c)

300

d)

75

4.

What is the average rate of change from x=0 to x=1

a)

-3

b)

3

c)

0

d)

2

5.

Which expression represents g(f(x)) if

f(x) = 2x - 8 and

g(x) = 4x

a)

8x - 32

b)

8x² - 32x

c)

8x - 8

d)

6x - 8

6.

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

a)

16

b)

4

c)

-4

d)

None of these.

7.

a)

136

b)

4

c)

8

d)

147

8.

What is f(g(3))?

a)

1/8

b)

8

c)

1/4

d)

1/2

9.

Find f(h(5)) based on the graphs of f(x) and h(x)

a)

-6

b)

-3

c)

6

d)

2

10.

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

(a)

11.

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

12.

Find the inverse of $f\left(x\right)=\frac{1}{4}x-7$

a)

f^-1(x) = 4x + 7

b)

f^-1(x) = -4x+28

c)

f^-1(x) = -4x - 7

d)

f^-1(x) = 4x+28

13.

$f\left(x\right)=\frac{x-2}{6}$
Find $f^{-1}\left(x\right)$

a)

$\frac{x-6}{2}$

b)

$6x+2$

c)

$2x+6$

d)

$6\left(x+2\right)$

14.

Find the correct order to find the inverse of f(x)= 2x-5

a)

y=2x-5

b)

2y-5=x

c)

2y= x+5

d)

$y=\frac{x+5}{2}$

e)

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

1)

2)

3)

4)

5)

15.

Which is f ^-1(x)?

a)

f^-1(x) = 3x + 5

b)

f^-1(x) = 3x - 5

c)

f^-1(x) = 3x - 15

d)

f^-1(x) = 3x + 15

16.

Are the following inverses of each other?

a)

True

b)

False

17.

10^log(k)=

a)

k

b)

10

c)

10^k

d)

1

18.

Evaluate the log:
log₃(1/9) =

a)

1/2

b)

2

c)

-2

d)

3

19.

Identify the asymptote of the transformed graph $\log_2\left(x+3\right)$ shown in red in the graph

a)

$x=-3$

b)

$x=3$

c)

$y=3$

d)

$y=-3$

20.

Match the following log functions to their horizontal shift (which way will the asymptote shift)

a)

$\ln\left(x\right)$

1.

No Horizontal Shift

b)

$\ln\left(x-4\right)$

2.

Shift Right

c)

$\ln\left(x+5\right)$

3.

Shift Left

21.

Identify the asymptote for the function ℎ(𝑥) = 𝑙𝑛(𝑥 − 1) + 3.

a)

$x=3$

b)

$x=-1$

c)

$y=1$

d)

$x=1$

22.

Which graph correctly shows the asymptote of $f(x)=\log(x+2)+3$

a)

b)

c)

d)

23.

Match the following graphs with their domains

a)

1.

Domian: x > -2

b)

2.

Domian: x > 3

c)

3.

Domian: x > 0

d)

4.

Domian: x > 2

24.

Of the functions shown, which is the ONLY possible function to describe the graph shown?

a)

$-\ln\left(x+3\right)$

b)

$-\ln\left(x-3\right)$

c)

$-\ln\left(x\right)-3$

d)

$-\ln\left(x\right)+3$

25.

What is the domain of $y=\log_3\left(x-3\right)-2$

a)

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

b)

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

c)

$\left(3,\infty\right)$

d)

$\left(-3,\infty\right)$

26.

What is the range of $y=\log_3\left(x-3\right)-2$

a)

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

b)

$\left(2,\infty\right)$

c)

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

d)

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

27.

log(xy²)

a)

logx+2logy

b)

logx+logy²

c)

logx-2logy

d)

logx+logy+log2

28.

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

a)

logx+logy

b)

xlogy

c)

log(x-y)

d)

logx-logy

29.

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

a)

logm-log3-logn

b)

3logm+logn

c)

3logm-logn

d)

3log(m-n)

30.

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

a)

log8+logx-logy-logz

b)

log8+logx-logy+logz

c)

log(8x)-log(yz)

d)

8logx-ylogz

31.

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)

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

32.

a)

ln(wvu⁵)

b)

ln(u + v + w⁵)

c)

ln(uvw⁵)

d)

ln(uvw)⁵

33.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

34.

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)

35.

Find the inverse of the equation

a)

y=2^(x+9)-5

b)

y=2^(x-9)-5

c)

y=2^(x+9)+5

d)

y=2^(x+5)-9

36.

a)

4

b)

-4

c)

1/4

d)

-1/4

37.

Rewrite 1.6^(x+2) = 14.1

a)

log_1.614.1 = x+2

b)

log_1.6(x+2) = 14.1

c)

log_14.1(x+2) = 1.6

d)

log_(x+2)1.6 = 14.1

38.

Rewrite log_x95 = 2.3

a)

x^2.3 = 95

b)

95^2.3 = x

c)

2.3⁹⁵ = x

d)

x⁹⁵= 2.3

39.

Rewrite 1.6^(x+2) = 14.1

a)

log_1.614.1 = x+2

b)

log_1.6(x+2) = 14.1

c)

log_14.1(x+2) = 1.6

d)

log_(x+2)1.6 = 14.1

40.

Solve the following for 'x';

log₆(3x - 2) = log₆(5x - 8)

a)

x = 3

b)

x = 2

c)

x = -1

d)

No Solution

41.

Re-Write the Logarithm Equation into Exponential Form
log_hw = d

a)

w = h^d

b)

w^d = h

c)

h = w^d

d)

h^w = d

42.

log (2 / 3) = ?

a)

log 2 + log 3

b)

log 2 / log 3

c)

log 2 - log 3

d)

2/3 * log 1

43.

Choose the graph that represents a logarithmic function.

a)

b)

c)

d)

44.

Rewrite the equation in exponential form.
$\log_8\left(512\right)=3$

a)

$8^{512}=3$

b)

$3^8=512$

c)

$8^3=512$

d)

$3^{512}=8$

45.

Evaluate the expression.
$\log_4\left(\frac{1}{64}\right)$

a)

3

b)

$-3$

c)

$\frac{1}{3}$

d)

16

46.

Evaluate the expression.
$\log_{49}\left(343\right)$

a)

2

b)

$\frac{3}{2}$

c)

$\frac{2}{3}$

d)

3

47.

Simplify the expression.
$\log_{13}\left(13^9\right)$

a)

9

b)

13

c)

$\frac{1}{9}$

d)

8

48.

Simplify the expression.
$18^{\log_{18}\left(23\right)}$

a)

18

b)

23

c)

$\frac{23}{18}$

d)

5

49.

Find the inverse function of $f\left(x\right)=5^x$

a)

$f^{-1}\left(x\right)\ =\ \log_5x$

b)

$f^{-1}\left(x\right)=\log_{5x}$

c)

$f^{-1}\left(x\right)=5\log x$

d)

$f^{-1}\left(x\right)=\log5x$

50.

Which equation is the inverse of the equation above?

a)

b)

c)

d)

51.

$\log_37$ is equivalent to

a)

$\frac{\log7}{\log3}$

b)

$\frac{\log3}{\log7}$

c)

$\log\left(3\cdot7\right)$

d)

$\log\left(\frac{7}{3}\right)$

52.

Use the horizontal line test to determine if the function has an inverse function.

a)

yes

b)

no

53.

Use the horizontal line test to determine if the function has an inverse function.

a)

yes

b)

no

54.

Determine if the function has an inverse function. If it does, then find the inverse function.

f\left(x\right)=\left(x-5\right)^2

a)

yes, $f^{-1}\left(x\right)=\sqrt{x-5}$

b)

yes, $f^{-1}\left(x\right)=\ x^2-10x+25$

c)

yes, $f^{-1}\left(x\right)=\sqrt{x}+5$

d)

no inverse

55.

Describe the translation that occurred: $w\left(x\right)=f\left(x-7\right)$

a)

Down 7

b)

Up 7

c)

Right 7

d)

Left 7

56.

Describe the translation that occurred: $m\left(x\right)=f\left(x+1\right)$

a)

Left 1

b)

Right 1

c)

Up 1

d)

Down 1

57.

Describe the translation from the blue dotted graph to the red graph.

a)

$f\left(x-4\right)-3$

b)

$f\left(x-4\right)+3$

c)

$f\left(x+4\right)+3$

d)

$f\left(x+4\right)-3$

58.

Which equation below is a quadratic that has been translated up 5 units?

a)

$f\left(x\right)=x^2-5$

b)

$f\left(x\right)=x^2+5$

c)

$f\left(x\right)=\left(x-5\right)^2$

d)

$f\left(x\right)=\left(x+5\right)^2$

e)

$f\left(x\right)=\sqrt{x}+5$

59.

Name the transformation from the function $y=\sqrt{x}$ to the function $y=-\sqrt{x+3}$ .

a)

Reflection over the y-axis, left 3.

b)

Reflection over the y-axis, right 3.

c)

Reflection over the x-axis, left 3.

d)

Reflection over the x-axis, right 3.

60.

Which function shows a reflection over the x-axis and a shift right 3 units?

a)

$-f\left(x-3\right)$

b)

$-f\left(x+3\right)$

c)

$f\left(-x+3\right)$

d)

$-f\left(x\right)-3$

61.

$-f\left(x+3\right)+4$

Describe the transformations:

a)

Shifted left 3 units
Shifted up 4 units

b)

Reflection over the y-axis
Shifted right 3 units
Shifted up 4 units

c)

Shifted right 3 units
Shifted up 4 units

d)

Reflection over the x-axis
Shifted left 3 units
Shifted up 4 units

62.

Describe the transformation: $f\left(x\right)=\frac{1}{3}x^2+2$

a)

Vertical compression by a factor of of 1/3
Up 2

b)

Vertical stretch by a factor of 1/3
Up 2

c)

reflection over the x-axis
Up 2

d)

Vertical compression by a factor of of 1/3

Right 2

63.

If the blue function is f(x)=√x, the red function must be

a)

g(x)=√(-x)

b)

g(x)=√(x-1)

c)

g(x)=√x-1

d)

g(x)=-√x

64.

Identify the transformation from the graph of f(x)=x²to the graph g(x)= -(x+5)²

a)

shifted up five units

reflection in x-axis

b)

shifted down five units

reflection in x-axis

c)

shifted left 5 units

reflection x-axis

d)

shifted right 5 units

reflection x-axis

65.

If the original function is f(x) then state the transformation that takes f(x) to g(x) = |-x + 3|

a)

Reflect over y-axis
Left 3

b)

Reflect over y-axis
Right 3

c)

Reflect over x-axis
Left 3

d)

Reflect over x-axis
Right 3

66.

Ash has $8,000 in a savings account. The interest rate is 3% compounded once a year.

To the nearest cent, how much will he have in his account in 4 years?

a)

$9,004.07

b)

$2,2848.80

c)

$9,011.94

d)

$8,242.71

67.

A sailboat that costs $5,950 decreases in value by 11% per year. How much will the boat be worth after 6 years?

a)

$5,884.00

b)

$5,178.97

c)

$2,992.96

d)

$2,957.04

68.

Emily’s parents put $1,500 in her bank account for college tuition. At an interest rate of 8.25% compounded semiannually,what will be the balance after 18 years?

a)

$6,273.50 frustrated

b)

$6,314.08 bewildered

c)

$6,385.72 pleased

d)

$6,427.94 tickled pink

69.

Mark took a loan out for $25,690 to purchase a truck. At an interest rate of 5.2% compounded monthly, how much total will he have paid after 5 years?

a)

$33,299.42 playing dodgeball

b)

$33,672.68 climbing trees

c)

$34,157.04 riding unicycles

d)

$34,710.88 flipping pancakes

70.

The Henley'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 after 30 years?

a)

$412,749.79 Labor Day

b)

$429,305.61 the 4th of July

c)

$471,259.24 Groundhog Day

d)

$494,546.99 Valentine’s Day

71.

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 interest will she earn in 10 years?

a)

$915.59 Rome

b)

$933.28 Sydney

c)

$979.81 Dublin

d)

$1,005.09 Paris

72.

Johnny takes an unknown amount of money and deposits it in a bank at an interest rate of 2%. He leaves the money in the account for 6 years, compounded quarterly. If the Johnny withdraws after 6 years is $455,125, what was the original amount of money he deposited?

a)

$403 780

b)

$404 138

c)

$406 362

d)

$436 870

73.

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

a)

x = 5

b)

x = -5

c)

x = 1/5

d)

x = -1/5

74.

You want to save $5,000 for future family vacation. If you assume you can get an interest rate of 4.3% compounded monthly, then how much will you need to invest NOW to reach your vacation goal in 3 years?

a)

$307,042,791

b)

$5,000

c)

$3,250

d)

$4,395.89

75.

Find Cos(A) as a decimal rounded the the nearest ten-thousandth.

(a)

76.

Find the value of x

a)

37.742

b)

10.598

c)

23.584

d)

12.497

77.

a)

29.237

b)

14.184

c)

11.082

d)

14.063

78.

Susan is flying a kite, which gets caught in the top of a tree. Use the diagram to estimate the height of the tree.

(a)

79.

$\cos\left(\theta\right)=?$

a)

$\frac{3}{5}$

b)

$\frac{4}{5}$

c)

$\frac{3}{4}$

d)

$\frac{4}{3}$

80.

Find the measure of the indicated angle.

a)

$6^{\circ}$

b)

$20^{\circ}$

c)

$43^{\circ}$

d)

$47^{\circ}$

81.

To the nearest whole degree.

a)

66^°

b)

24^°

c)

22^°

d)

^37°

82.

Match the following

a)

$\sin\left(\theta\right)=$

1.

$\frac{1}{\csc\left(\theta\right)}$

b)

$\cos\left(\theta\right)=$

2.

$\frac{1}{\sec\theta}$

c)

$\tan\left(\theta\right)=$

3.

$\frac{1}{\cot\left(\theta\right)}$

d)

$\sin^{-1}\left(\frac{opp}{hyp}\right)=$

4.

$\theta$

e)

$a^2+b^2=$

5.

$c^2$

83.

Bo is flying a kite, holding his hands a distance of 3.5 feet above the ground and letting all the kite’s string play out. He measures the angle of elevation from his hand to the kite to be $29\degree$ . If the string from the kite to his hand is 110 feet long, how many feet is the kite above the ground? Round your answer to the nearest hundredth of a foot if necessary.

(a)

84.

Use a calculator to find the value of the trig function.

$\sin50\degree$

(a)

85.

Use a calculator to find the value of the trig function.

$\cos65\degree$

(a)

86.

Use a calculator to find the measure of the angle.

$\sin x=0.9781$

(a)

87.

Use a calculator to find the measure of the angle.

$\cos x=0.9744$

(a)

88.

Find the measure of the angle indicated.

a)

$43\degree$

b)

$54\degree$

c)

$36\degree$

d)

$47\degree$

89.

A tourist views a deer from a height of 45 feet. The horizontal distance between the tourist and the deer is 130 feet. At what angle (x) should the tourist hold his camera to photograph the deer? Round your answer to the nearest degree.

a)

19 degrees

b)

45 degrees

c)

71 degrees

d)

138 degrees

90.

Solve for the missing distance.

a)

18.9

b)

19.5

c)

47

d)

27.5

91.

Choose the correct ratio.

a)

sin(37)=x/14

b)

cos(37)=x/14

c)

tan(37)=x/14

d)

sin(37)=14/x

92.

A hawk sitting on a tree branch spots a mouse on the ground 15 feet from the base of the tree. The hawk swoops down toward the mouse at an angle of 30 degrees. What is the distance from the tree branch to the mouse?

a)

7.5 ft

b)

15 ft

c)

26 ft

d)

30 ft

Exam Review 5/9/24

Total questions: 92

Worksheet time: 4hrs 27mins

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