Free Printable Final Exam Review

1.

Describe the transformation that occurred

p(x) = f(x + 3)

a)

Right 3 units

b)

Vertical Stretch

c)

Up 3 units

d)

Left 3 units

2.

Describe the transformation that occurred.

h(x) = f(x) + 2

a)

up 2 units

b)

left 2 units

c)

Vertical Strech

d)

right 2 units

3.

Describe the transformation that occurred

g(x) =2f(x)

a)

Up 2 units

b)

vertical compression

c)

vertical stretch

d)

Right 2 Units

4.

-f(x) - 2

a)

reflection over y-axis, shift down 2

b)

reflection over y-axis, shift right 2

c)

reflection over x-axis, shift right 2

d)

reflection over x-axis, shift down 2

5.

Write in function form: translation 3 units right

a)

g(x) = f(x − 3)

b)

g(x) = f(x) − 3

c)

g(x) = -3f(x)

d)

g(x) = f(-3x)

6.

vertical reflection, horizontal stretch

a)

g(x) = ½f(-x)

b)

g(x) = -f(¼x)

c)

g(x) = -3f(x)

d)

g(x) = -f(4x)

7.

What is the range of the graph?

a)

[-7, 5)

b)

(-3, 1]

c)

[-3, 1)

d)

(-7, 5]

8.

What is the domain?

a)

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

b)

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

c)

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

d)

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

e)

None of the answer choices

9.

Which graph does NOT pass the vertical line test?

a)

Graph 1

b)

Graph 2

c)

Graph 3

d)

Graph 4

10.

What is the range of the graph?

a)

(-∞,∞)

b)

[-1,0]

c)

[-1,3]

d)

[3,∞)

11.

What is the range of the graph?

a)

[1, ∞)

b)

(1, ∞)

c)

(-∞, ∞)

d)

none of these

12.

Write the following in interval notation
x < 8

a)

(8, ∞)

b)

(8, -∞)

c)

(-∞, 8)

d)

[-∞, 8]

13.

Describe the end behavior of the graph.

a)

x → -∞, f(x) → ∞ and x→∞, f(x) →⁻∞

b)

x → -∞, f(x) → ∞ and x→∞, f(x) →∞

c)

x → -∞, f(x) → ∞ and x→∞, f(x) → 0

d)

x → -∞,f(x) → -∞and x→ ∞, f(x) → ∞

14.

What is the degree of the polynomial?

a)

2

b)

3

c)

4

d)

5

15.

Describe the end behavior of the graph.

a)

x →∞, y→⁻∞ and x →⁻∞,y→⁻∞

b)

x →∞, y→∞ and x→⁻∞, y→∞

c)

x →∞, y→∞ and x→⁻∞, y→0

d)

x →∞,y→∞ and x→⁻∞, y→⁻∞

16.

What is the degree?

a)

Positive

b)

Negative

c)

Odd

d)

Even

17.

What is the degree?

a)

Positive

b)

Negative

c)

Odd

d)

Even

18.

What is the leading coefficient?

a)

Positive

b)

Negative

c)

Odd

d)

Even

19.

Solve x²= -16

a)

x = -4, 4

b)

x = -4,0, 4

c)

x = -4i, 4i

20.

What is the vertex for the parabola represented by the equation
y = 2(x + 3)² - 8?

a)

(3, 8)

b)

(3, -8)

c)

(-3, 8)

d)

(-3, -8)

21.

How many zeros does this parabola have?

a)

3

b)

2

c)

0

d)

1

22.

What is another name for the x-intercepts of a quadratic?

a)

y-intercept

b)

Zeros

c)

x-axis

d)

They don't have another name

23.

What does i² = ?

a)

-1

b)

√-1

c)

1

d)

-√1

24.

Multiply
(2i)(3i)

a)

5i

b)

-5

c)

6i

d)

-6

25.

Find the y-intercept of f(x) = 2x²- 2x + 1

a)

2

b)

-2

c)

1

d)

-1

26.

What is the vertex of the quadratic function:
y = x² - 6x + 11?

a)

(3,2)

b)

(-3,-2)

c)

(-3,2)

d)

(3,-2)

27.

Identify the vertex and whether the graph opens up or down.

a)

(-1, 4); opens up

b)

(-1, 4); opens down

c)

(1, 4); opens up

d)

(1, 4); opens down

28.

Factor completely
k² -2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

29.

Solve by factoring
x² + 13x + 12 = 0

a)

x = -12, -1

b)

x = 12, 1

c)

x = 13, 1

d)

x = -13, -1

30.

What is the equation for axis of symmetry?

a)

y=3

b)

x=3

c)

x=5

d)

x=1

31.

What is the axis of symmetry of:y=2x²-4x+9

a)

x = 1

b)

x = -1

c)

x = -2

d)

x = 4

32.

Classify by degree of polynomial:
3x³ – 6x

a)

Constant

b)

Linear

c)

Quadratic

d)

Cubic

33.

Add the polynomials:
(3x³+3x²–4x+5) + (x³–2x²+x–4)

a)

4x³ + 1x² – 3x + 1

b)

2x³ + 1x² - 5x + 9

c)

6x³ + 1x - 1x² - 3

d)

3x⁵ +1x - 1x⁵ - 3x

34.

Simplify the expression.
(4n⁴-8n+4) - (8n²+4n⁴+1)

a)

-8n² - 8n + 3

b)

-7n² - 8n + 3

c)

-6n²- 8n + 3

d)

-7n² - 4n + 3

35.

Multiply:
(4x+1)(5x−2)

a)

20x² + 3x − 2

b)

20x² − 11x + 5

c)

20x² − 18x + 2

d)

20x² − 3x − 2

36.

(5x+2)(x²-3x+6)

a)

5x³- 17x²+24x +12

b)

5x³+ 17x² - 24x +12

c)

5x³ - 13x² + 24x +12

d)

5x³ +13x² - 24x - 12

37.

A rectangle has width (2x + 3) and length (2x - 4). What is the perimeter of the rectangle?

a)

4x- 12

b)

4x- 1

c)

8x- 2

d)

4x²- 2x - 12

38.

Find the area of a rectangle with length (x - 5) and width (3x + 1).

a)

3x²+16x-5

b)

3x²-14x+5

c)

3x²-14x-5

39.

Divide:

(4x² - 24x + 35) / (2x - 5)

a)

2x - 7

b)

2x - 12

c)

2x + 12

d)

2x + 7

40.

Divide using synthetic division
(2x³ - 5x - 7) ÷ (x - 2)

a)

2x³ - 4x² + 3x - 13

b)

2x³ + 4x² +3x - 1

c)

2x² - 4x + 3 - 13/x-2

d)

2x² + 4x + 3 - 1/x-2

41.

Even Multiplicities have which of the following effects on the x-axis?

a)

touches and bounces back

b)

wiggle

c)

crosses the x-axis

42.

Which root has even multiplicity?

a)

1

b)

-4

c)

-1

d)

2

43.

What is the equation in factored form of this graph?

a)

f(x) = (x-4)(x-1)²(x+2)(x+4)

b)

f(x) = (x-4)(x+1)²(x+2)(x+4)

c)

f(x) = (x-4)(x-1)²(x-2)(x+4)

d)

f(x) = (x+4)(x+1)²(x-2)(x-4)

44.

What are the zeros of the polynomial function?
y = x(x - 6)(x + 5)

a)

0, 6, -5

b)

6, -5

c)

0, -6, 5

d)

1, -6, 5

45.

What is the Degree of this polynomial:
f(x)= x³(x + 3)²(x – 5)

a)

Degree: 6

b)

Degree: 5

c)

Degree: 3

d)

Degree: 2

46.

f(x) = (x+2)(x-3)²(x-4)

Which choice best describes the zeros?

a)

-2, 3 (multiplicity 2), 4

b)

-2 (multiplicity 2), 3, 4

c)

2, -3 (multiplicity 2), -4

d)

2 (multiplicity 2), -3, -4

47.

If the graph of a function crosses the x-axis, what does that mean about the multiplicity of that zero?

a)

Even

b)

Odd

c)

None

48.

Which one of these are not a zero of $f\left(x\right)=-2x\left(3x+1\right)^2\left(x+7\right)^7$

a)

-2

b)

0

c)

$-\frac{1}{3}$

d)

-7

49.

What is the multiplicity of the zero x=-5 for the function $f\left(x\right)=x^2\left(x-1\right)^4\left(x+5\right)$ ?

a)

1

b)

2

c)

3

d)

4

50.

Find the inverse of f(x) = -4x - 12

a)

f^-1(x) = 4x - 3

b)

f^-1(x) = -1/4x - 3

c)

f^-1(x) = 1/4x + 3

d)

f^-1(x) = -4x - 3

51.

What does it mean to find the inverse of a function?

a)

the x's and y's are switched

b)

the x's and y's are divided by 2

c)

the x's and y's are made negative

d)

the x's and y's are the same

52.

If f(x)=x+5, what is f^-1(x)?

a)

(x + 5)²

b)

x - 5

c)

(x + 5)^-1

d)

undefined

53.

If the equation of f(x) goes through (1, 4) and (4, 6), what points does f^-1(x) go through?

a)

(1, 4) and (4, 6)

b)

(-4, -1) and (-6, -4)

c)

(-1, -4) and (-4, -6)

d)

(4, 1) and (6, 4)

54.

Determine f^-1(2) given the following information about f(x) f(1) = -3 f(2) = -2 f(-1) = 2 f(3) = -1

a)

1

b)

-1

c)

2

d)

-2

55.

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

a)

yes

b)

no

56.

Is the relation shown a function?

a)

YES

b)

NO

57.

If the decay rate is 20%, which of the following represent the decay factor?

a)

0.2

b)

0.8

c)

1.2

d)

1.8

58.

If the growth rate is 80%, what is the growth factor?

a)

0.2

b)

0.8

c)

1.2

d)

1.8

59.

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)

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

60.

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)

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

61.

Jack invest $600 earning 5% interest rate. How much will he have after 5 years?

a)

$630

b)

$729.30

c)

$765.77

d)

$4556.25

62.

Write the expression in exponential form:
∛x²

a)

x^3/2

b)

x^2/3

c)

x^1/2

d)

x^1/3

63.

Simplify the expression:
36^1/2

a)

6

b)

36

c)

-6

d)

1296

64.

What is the value of 27^⅓?

a)

27

b)

9

c)

3

d)

1/3

65.

Simplify the following expression:

a)

5

b)

25

c)

125

d)

625

66.

a)

4^4/3

b)

4^3/4

c)

2^4/3

d)

2^3/4

67.

Solve for x

a)

x = -3

b)

x = -3, 5

c)

x = 3, 5

d)

x = 5

68.

Solve for X:

a)

a x=1/2

b)

b x=10

c)

c x=4

d)

d x=12

69.

Evaluate the following logarithm:

log₃27

a)

3

b)

2

c)

-3

d)

¹/₃

70.

Evaluate the following logarithm:

log₅5

a)

1

b)

0

c)

-1

d)

¹/₂

71.

Evaluate.
log₆(¹/₂₁₆)

a)

3

b)

¹/₃

c)

-¹/₃

d)

-3

72.

Rewrite log₂8 = 3 in exponential form

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

73.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

74.

Solve for x: $\log_2\ \frac{x}{5}=\ 3$

a)

40

b)

8/5

c)

30

d)

6/5

75.

Write the logarithm expression as a single logarithm

log₅4 + log₅3

a)

log₅7

b)

log₅12

c)

log₇5

d)

3log₅4

76.

Write the logarithm expression as a single logarithm

log₆25 - log₆5

a)

log₆125

b)

log₅20

c)

log₆5

d)

log₆30

77.

Write as one logarithm. Simplify, if possible.

(log 3 - log 6) + log 2

a)

log 4

b)

log 2

c)

log 1

d)

log 6

78.

What equation can be used to solve for x?

a)

Sin(40°)= x/40

b)

Sin(40º)=x/19

c)

Cos(40º)=x/19

d)

Tan(40°)=19/x

79.

Find x round to the nearest tenth.

a)

46.1

b)

4.9

c)

16.4

d)

26.9

80.

a)

14/48

b)

48/50

c)

14/50

d)

48/14

81.

How many radians does a circle have?

a)

360 degrees

b)

2pi radians

c)

pi radians

d)

^{2 radians}

82.

Convert 150⁰ to radians

a)

5π/6

b)

3π/4

c)

7π/6

d)

2π/3

83.

What is 7π/4 radians in degrees?

a)

300

b)

135

c)

315

d)

45

84.

What is the reference angle for $\frac{15\pi}{11}$ ?

a)

4π

b)

$\frac{4\pi}{11}$

c)

$\frac{7\pi}{11}$

85.

Find x.

a)

10

b)

10√3

c)

10√2

d)

20

86.

Find x.

a)

22

b)

11√3

c)

11√2

d)

11

87.

Determine the value of x.

a)

x = 10√2

b)

x = 10

c)

x = 5√3

d)

x = 5√6

88.

Which angle is coterminal with 110°

a)

-250

b)

70

c)

20

d)

-70

89.

What is cos $60\degree$ ?

a)

1

b)

√3/2

c)

√2/2

d)

1/2

90.

In right triangle ABC,<C is a right angle and $\sin B=\frac{4}{5}$ .
Find $\cos B$

a)

1/5

b)

3/5

c)

3/4

d)

4/3

91.

What is reference angle for 280°

a)

10

b)

100

c)

80

d)

40

92.

What is tan $210\degree$ ?

a)

√3

b)

1

c)

-√3/3

d)

√3/3

93.

What is cos 0 ?

a)

0

b)

1

c)

-1

d)

1/2

94.

If sin A is negative and cos A is positive, what quadrant does the terminal side of <A lie?

a)

I

b)

II

c)

III

d)

IV

95.

What is the tan $\frac{\pi}{2}$ ?

a)

0

b)

1

c)

undefined

d)

-1

96.

The $\tan\ 300\degree$ must be:

a)

positive

b)

negative

97.

If cosθ = √2/2, which could be the measure of θ?

a)

30

b)

45

c)

60

d)

90

98.

What is the sin270?

a)

0

b)

1

c)

-1

d)

undefined

99.

6^3x - 3 = 56

(hint you must use logarithms!)

a)

2.2757

b)

1.3592

c)

0.7586

d)

0.5903

100.

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation
s(t) = –16t² + 64t + 80.
What will be the object's maximum height?

a)

2 ft

b)

80 ft

c)

144 ft

d)

64 ft

Final Exam Review

Total questions: 100

Worksheet time: 9hrs 40mins

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