Free Printable Final Pre-College Review

1.

What is the amplitude of the graph?

a)

1

b)

3

c)

6

d)

9

2.

what is the amplitude of y=3sin(7x)-2

a)

7

b)

-2

c)

3

d)

6

3.

What is the period of y=4cos5x

a)

2π/5

b)

π

c)

5

d)

5π

4.

What is the period of y = 4Cos(2x)?

a)

4π

b)

π

c)

2π

d)

π/2

5.

What is the amplitude and period of y = 2sin(3x)

a)

2 and 3

b)

3 and 2

c)

2,2π/3,

d)

2π/3, 2

6.

What is the amplitude and period of y = 2sin(πx)

a)

2 and 2

b)

π and 2

c)

2 and π

d)

2π and 2

7.

The __________ measure the distance from the midline to the max or min of the function.

a)

Amplitude

b)

Phase Shift

c)

Vertical Translation

d)

Horizantal Translation

8.

Assuming no transformations, what type of function is this?

a)

sin

b)

cos

c)

tan

d)

cot

9.

The horizontal length required to complete one cycle.

a)

Period

b)

Cycle

c)

Axis of Oscillation

d)

Amplitude

10.

what is the amplitude of y=3sin(7x)-2

a)

7

b)

-2

c)

3

d)

6

11.

which value represents amplitude in the function y = asin(bx-h) + k

a)

a

b)

b

c)

h

d)

k

12.

What is the period of y=4cos5x

a)

2π/5

b)

π

c)

5

d)

5π

13.

What is the period of y=4cos(5x)

a)

2π/5

b)

π

c)

5π/2

d)

5π

14.

Sine or Cosine?

a)

y=sinx

b)

y=cosx

15.

Sine or Cosine?

a)

y=sinx

b)

y=cosx

16.

What is the domain and range of y=sinx?

a)

D: (-∞, ∞)
R: [-1, 1]

b)

D: (-∞, ∞)
R: [-π, π]

c)

D: (∞, -∞)
R: [-1, 1]

d)

D: (-∞, ∞)
R: [-∞, ∞]

17.

What is the period?

a)

π/4

b)

π/2

c)

3π/4

d)

π

18.

What does a negative A value cause?

a)

A negative amplitude

b)

A reflection across the Y axis

c)

No effect

d)

A reflection across X axis

19.

What is the equation of the graph shown?

a)

y=1/2cos2x

b)

y=1/2sin4x

c)

y=1/2cos4x

d)

y=4cos1/2x

20.

What is the equation of the blue graph?

a)

y = 2sin x

b)

y = sin(2x)

c)

y = sin(x + 2)

d)

y = sin x - 2

21.

Where does the graph of cosine begin?

a)

(0,0)

b)

(0,1)

c)

(0, Pi)

d)

(1, Pi)

22.

Where does the graph of y=sin(x) begin its first cycle?

a)

(0,0)

b)

(1,0)

c)

(0,Pi)

d)

(1, Pi)

23.

Write an equation of a sine function with a period of π and amplitude of 7.

a)

y=7sin2πx

b)

y=7sinπx

c)

y=2sin7x

d)

y=7sin2x

24.

What is the equation of the graph?

a)

y = 2 cos x

b)

y = sin x

c)

y = 2 sin x

d)

y = sin 2x

25.

Which function represents the graph?

a)

f(x) = 3 sin x

b)

f(x) = 3 cos x

c)

f(x) = sin ( ⅓ x)

d)

f(x) = sin (3 x)

26.

What is the correct graph of the function?

a)

b)

c)

d)

27.

What is the correct graph of the function?

a)

b)

c)

d)

28.

The polynomial
f(x) = 5x⁴ + 2x³ + 2x − 7 can have, at most, how many solutions?

a)

5

b)

4

c)

3

d)

2

29.

In the above graph, which root has a multiplicity of 2?

a)

-1

b)

-3

c)

-120

d)

4

30.

What is the leading coefficient?

a)

Positive

b)

Negative

31.

f(x)= x²(x – 2)³(x – 7)

Find and select each real zero and its multiplicity

a)

0 (Mult of 2), 2 (Mult of 3), 7 (mult 1)

b)

2 (Mult of 3), 7 (mult 1)

c)

0, 2, 7

d)

2 (mult of 2), 7 (mult of 3)

32.

What is the leading coefficient?

a)

Positive

b)

Negative

c)

Odd

d)

Even

33.

Divide: $\frac{x^4+2x^3+2x+4}{x+2}$

a)

$x^3+2x^2$

b)

$x^3+2$

c)

$x^3+4x^2+8x+18+\frac{42}{x+2}$

d)

$x^3+4x^2+10x+24$

34.

Divide: $\frac{2x^4-9x^3+21x^2-26x+12}{2x-3}$

a)

$x^3-3x^2+6x-4$

b)

$2x^3-6x^2+12x-8$

c)

$x^4-3x^3+6x^2-4x$

d)

$2x^4-6x^3+12x^2-8x^{ }$

35.

Divide: $\frac{x^3-12x^2+47x-60}{x-3}$

a)

$x^2-9x+20$

b)

$x^3-9x^2+20x$

c)

$x^2-15x+92+\frac{216}{x-3}$

d)

$x^2+9x+20$

36.

Divide: $\frac{3x^3-4x^2-9x+10}{x-2}$

a)

$3x^2+2x-5$

b)

$3x^3+2x^2-5x$

c)

$3x^2-10x^{ }-29-\frac{48}{x-2}$

d)

$3x^2-10x-29+\frac{48}{x-2}$

37.

Divide: $\frac{27x^3+64}{3x+4}$

a)

$27x^2-36x+48$

b)

$9x^2-12x+16$

c)

$27x^2+28x$

d)

$27x^2+28$

38.

What is the proper way to write the answer for the following problem?

a)

2x³-x²-25x-12

b)

2x⁴-x³-25x²-12x+0

39.

For synthetic division, what would be the number in the left hand box?

a)

0

b)

1

c)

2

d)

3

40.

Let
f(x) = 4x^2 -33x -27.
Is k = 9 a zero of the function?

a)

yes

b)

no

41.

a)

x+7

b)

x+2

c)

X-10

d)

X-7

42.

Factor
n²-13n+40

a)

(n-5)(n-8)

b)

(n+5)(n-8)

c)

(n-5)(n+8)

d)

(n+6)(n+1)

43.

What do the "Zeros" represent on a quadratic equation graph?

a)

x-intercepts

b)

y-intercepts

c)

vertex

d)

focus

44.

What is the factored form of 25x²-9

a)

(5x+3)(5x-3)

b)

(x+5)(x-3)

c)

(x-3)(x+5)

d)

(5x+3)(3x+5)

45.

Factor (hint...take out the greatest common factor first)
2c² + 2c - 84

a)

(c-6)(2c+14)

b)

(c+7)(2c-12)

c)

(c-4)(2c+21)

d)

2(c+7)(c-6)

46.

a)

y = ^_(x + 2)(x - 1)²

b)

y = -(x - 2)(x + 1)²

c)

y = (x - 2)(x + 1)²

d)

y = -x³

47.

a)

(-2.55, 0), (2.55, 0)

b)

(-3, 0), (-2, 0), (2, 0), (3, 0)

c)

(0, 36)

d)

(0, -3), (0, -2), (0, 2), (0, 3)

48.

If you know 3 and 2i are roots of a polynomial function, state the polynomial factors.

a)

(x + 3) , (x + 2i)

b)

(x - 3), (x -2i), (x + 2i)

c)

(x - 3), (x + 3), (x - 2i), (x + 2i)

d)

(x -3 - 2i), (x + 3 - 2i)

49.

f(x) = 2x³ - 3x² + 4x -10

What is the degree of f(x)?

a)

3

b)

2

c)

1

d)

0

50.

The degree of the polynomial determines the max number of roots.

a)

True

b)

False

51.

What is another way to say "where a function crosses the x-axis"?

a)

x-intercept

b)

zero

c)

root

d)

all of these.

52.

In the above graph complete the following end behavior:

As x --> +∞, f(x) --> ____

As x --> -∞, f(x) --> ____

a)

-∞

b)

+∞

-∞

c)

-∞

+∞

d)

+∞

53.

In the above graph complete the following end behavior:
As x --> +∞, f(x) --> ____
As x --> -∞, f(x) --> ____

a)

-∞

b)

+∞

-∞

c)

-∞

+∞

d)

+∞

54.

List the zero(s) of the function

a)

0

b)

0, -1

c)

1

d)

-1

55.

List the zero(s) of the function

a)

-4, 2, 4

b)

-4, -1, 2, 4

c)

-1, 2, 4

d)

-1

56.

The following polynomial should have what type of end behavior?

f\left(x\right)=-3x^4-2x+1

a)

Left: $\uparrow$ Right: $\downarrow$

b)

Left: $null$ Right: $\uparrow$

c)

Left: $\downarrow$ Right: undefined

d)

Left: $\downarrow$ Right: $\uparrow$

57.

The following polynomial should have what type of end behavior?

f\left(x\right)=2x^3-x+5

a)

Left: $\uparrow$ Right: $\downarrow$

b)

Left: $null$ Right: $\uparrow$

c)

Left: $\downarrow$ Right: undefined

d)

Left: $\downarrow$ Right: $\uparrow$

58.

What is the leading coefficient of the polynomial?

f\left(x\right)=x^4-x^3+3x

a)

1

b)

4

c)

0

d)

3

59.

What is the degree of the polynomial?

f\left(x\right)=-x^3+x

a)

-1

b)

1

c)

0

d)

3

60.

What is the degree of the polynomial?

f\left(x\right)=9x^5-x^4+2x

a)

5

b)

9

c)

4

d)

1

61.

(2x³ - 3x² + 2x - 8) + (-6x³ + 5x² + 4x - 7)

a)

-4x³ + 2x² + 6x - 15

b)

-4x⁶ + 2x⁴ + 6x² - 15

c)

8x³ - 8x² - 2x - 1

d)

-4x³ + 2x² + 6x - 1

62.

sin 2π/3

a)

1/2

b)

-1/2

c)

√3/2

d)

-√3/2

63.

sin 7π/6

a)

1/2

b)

-1/2

c)

√3/2

d)

-√3/2

64.

cos 4π/3

a)

-√3/2

b)

√3/2

c)

1/2

d)

-1/2

65.

cos 5π/6

a)

-1/2

b)

1/2

c)

√3/2

d)

-√3/2

66.

sin π/4

a)

√2∕2

b)

1/2

c)

√3/2

d)

0

67.

What are the coordinates of 60° on the unit circle?

a)

(0, 1)

b)

(1/2, √3/2)

c)

(√3/2, 1/2)

d)

(√2/2, 1/2)

68.

sinθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

69.

What is sin(0^o)?

a)

1

b)

-1

c)

0

d)

√2/2

70.

This rational function is undefined at...

a)

x = 4

b)

x = -4

c)

x = 0

d)

x = 5

71.

A vertical asymptote always has the equation...

a)

x = __

b)

y = __

72.

Which rational function has a vertical asymptote at x = -3

a)

$y=\frac{1}{x-3}$

b)

$y=\frac{1}{x+3}$

c)

$y=\frac{1}{3}$

d)

$y=\frac{3}{x}$

73.

The rational function, $f\left(x\right)=3+\frac{2}{x-4}$ has a horizontal asymptote at...

a)

y = -4

b)

y = 2

c)

y = 3

d)

y= 4

74.

What is the equation of this rational function

a)

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

b)

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

c)

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

d)

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

75.

What's the horizontal asymptote of the function?

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

a)

y = 3

b)

No horizontal asymptote

c)

y = 0

d)

y = 2

76.

Rewrite $g\left(x\right)=\frac{x+3}{x}$

a)

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

b)

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

c)

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

d)

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

77.

What type of function is this?

a)

Polynomial

b)

Quadratic

c)

Rational

d)

Radical

78.

A vertical asymptote is found by setting the _________= to zero and solving for x

a)

Numerator

b)

Denominator

c)

Right side

d)

Left side

79.

What are the asymptotes?

a)

x = -3 y = 1

b)

x = 3 y = 1

c)

x = -3 y = -1

d)

x = 3 y = -1

80.

What is the horizontal asymptote?

a)

x = 2

b)

y = 2

c)

x =-2

d)

y=-2

81.

Given

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

a)

11x² - 1

b)

5x⁴ + 6x² - 1

c)

5x² + 6x - 1

d)

5x² + 8x - 1

82.

Given f(x) = 3x² - 2x + 1 and g(x) = x - 4, find (f⋅g)(x).

a)

3x³ - 10x² - 7x - 4

b)

3x³ - 14x² + 9x - 4

c)

3x² - x - 3

d)

3x³ + 14x² - 9x - 4

83.

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

a)

19

b)

23

c)

-10

d)

None of these.

84.

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

a)

16

b)

4

c)

-4

d)

None of these.

85.

When 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

86.

Evaluate the function for the given inputs.
For f(x) = -2x + 4,
find f(x) when x = -5

a)

f(-5) = -6

b)

f(-5) = -3

c)

f(-5) = 14

d)

f(-5) = 2

87.

f(x)=x²-2x+1
Evaluate the function for f(-1).

a)

f(-1)=4

b)

f(-1)=0

c)

f(-1)=2

d)

f(-1)=-1

88.

a)

9 - 8/3

b)

9 + 8/3

c)

3

d)

1/3

89.

Find f[g(5)]

a)

30

b)

242

c)

92

d)

2

90.

If f(x) = 3x-1 and g(x) = x²+2,

what is (f ° g)(x) ?

a)

3x² +5

b)

x² +1

c)

3x² +1

d)

3x² +6

91.

g(x)=3x+4
h(x)=3x-1
Find (g∘h)(x)

a)

-9x+11

b)

4x²+4x

c)

9x+1

d)

9x+11

92.

f(g(x))

a)

3x - 16

b)

3x - 2

c)

3x - 26

d)

4x - 2

93.

If f(x) = x-5 and g(x) = 3x²-1,

what is (f ° g)(x) ?

a)

3x²-5

b)

3x²-1

c)

3x²-4

d)

3x²-6

94.

f(x) = x²+9
g(x) = x-9
Find f(x)-g(x).

a)

x²+x+9

b)

x²-x+9

c)

x²-x

d)

x²-x+18

95.

a)

b)

c)

d)

96.

State the range of the graphed function.

a)

-2 ≤ 𝒚 ≤ 1

b)

-2 ≤ 𝒚 < 1

c)

-3 ≤ 𝒙 < 4

d)

-3 < 𝒙 ≤ 4

97.

State the domain of the graphed function.

a)

-2 ≤ 𝒙 < 1

b)

-2 ≤ 𝒚 < 1

c)

-3 ≤ 𝒙 < 4

d)

-3 < 𝒙 ≤ 4

98.

What is the range of the function?

a)

(- $\infty$ , $\infty$ )

b)

[0,3]

c)

[-3,3]

d)

(0,3)

99.

What is the domain of this relation?

a)

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

b)

[-6,2]

c)

[-5,0]

d)

[-5,5]

e)

[-6,4]

100.

What is the range of this function?

a)

[-3,3]

b)

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

c)

{-2}

d)

{-3,-2,-1,1, 2, 3}

e)

[-2]

101.

What is the range of this function?

a)

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

b)

[-7,6]

c)

[0,2]

d)

[-5,4]

e)

[-4,4]

102.

What is the range of this relation?

a)

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

b)

[-4, $\infty$ )

c)

[-4,-1]

d)

{-4,-2,-1}

103.

What is the domain of this relation?

a)

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

b)

{-3, -1, 1, 3}

c)

[-3,3]

d)

{-3, -2, 1, 3}

104.

What is the range of this function?

a)

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

b)

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

c)

[-2, 4]

d)

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

105.

What is the domain of this function?

a)

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

b)

(1,4)

c)

[1,4]

d)

$\left[4,\ \infty\right)$

106.

What is the range of this relation?

a)

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

b)

[-5,0]

c)

[-6,-2]

d)

(-5, 0)

e)

(-6,-2)

107.

What is the range of this relation?

a)

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

b)

[0, 3]

c)

[-1,5]

d)

[1,3]

108.

What is the domain of this function?

a)

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

b)

[-3, 2]

c)

[2, -3]

d)

{-3,2}

109.

What is the domain?

a)

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

b)

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

c)

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

d)

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

e)

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

110.

Which parent function matches the graph?

a)

y = |x|

b)

y = x

c)

y = x²

d)

y = 2^x

111.

What type of function is shown?

a)

absolute value

b)

quadratic

c)

linear

d)

exponential

112.

What type of function is shown?

a)

linear

b)

quadratic

c)

square root

d)

absolute value

113.

Name the parent function.

a)

linear

b)

quadratic

c)

cube root

d)

cubic

114.

Name the parent function.

a)

constant

b)

square root

c)

linear

d)

absolute value

115.

Which equation below is a quadratic function translated up 5 units?

a)

y = x² + 5

b)

y = (x + 5)²

c)

y = 5x²

d)

y = -x² - 5

116.

What type of function is shown?

a)

cube root

b)

square root

c)

logarithm

d)

exponential

117.

Which equation below is a quadratic function translated left 4 units?

a)

y = x² + 4

b)

y = (x + 4)²

c)

y = (x - 4)²

d)

y = 4x²

118.

Which equation is a quadratic function reflected over the x-axis and shifted up 2.

a)

y = x² + 2

b)

y = -x² + 2

c)

y = x² - 2

d)

y = -(x + 2)²

119.

Describe the transformation

a)

left 2 up 5

b)

right 2 up 5

c)

left 2 down 5

d)

right 2 down 5

120.

Which equation is an absolute value graph shifted right 5 units?

a)

y = |x - 5|

b)

y = |x + 5|

c)

y = |x| + 5

d)

y = -5|x|

121.

Tell how the graph transformed.
y = (x - 3)²

a)

Translated right 3

b)

Translated left 3

c)

Translated up 3

d)

Translated down 9

122.

Describe the transformation.

a)

up 3

b)

down 3

c)

left 3

d)

right 3

123.

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

124.

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

125.

Describe the transformation that occurred.

w(x) = f(x - 7)

a)

Down 7

b)

Up 7

c)

Right 7

d)

vertical compression

126.

Describe the transformation that occurred

m(x) = f(x + 1)

a)

Left 1 Unit

b)

Right 1 unit

c)

vertical stretch

d)

up 1 unit

127.

Describe the transformation that occurred

k(x) = f(x) - 9

a)

vertical compression

b)

Down 9 units

c)

Left 9 units

d)

Right 9 Units

128.

Describe the transformation that occurred

g(x) =2f(x)

a)

Up 2 units

b)

vertical compression

c)

vertical stretch

d)

Right 2 Units

129.

Describe the transformation that occurred

h(x) = 1/5f(x)

a)

Up 5 Units

b)

vertical compression

c)

vertical stretch

d)

Down 5 Units

130.

Describe the transformation that occurred

s(x) = 7f(x)

a)

vertical compression

b)

Up 7 Units

c)

Over 7 Units

d)

vertical stretch

131.

Describe the transformation of the equation below from the parent function of y = I x I
y = I x - 4 I

a)

Left 4

b)

Right 4

c)

Up 4

d)

Down 4

132.

What causes the graph of y = x² to open downward?

a)

multiply the x² by a fraction

b)

multiply the x² by a decimal

c)

multiply the x² by a negative number

d)

multiply the x² by a number greater than 1

133.

What are the transformations?
y=(x-2)³+4

a)

Horz shift right 2 Vert shift up 4

b)

Horz shift left 2 Vert shift up 4

c)

Horz shift right 2 Vert shift down 4

d)

Horz shift left 2 Vert shift up 4

134.

Describe the transformation from dotted to solid.

a)

f(x + 4)

b)

f(x - 4)

c)

f(x) + 4

d)

f(x) - 4

135.

Describe the transformation from dotted to solid.

a)

f(x + 5) + 3

b)

f(x +3) + 5

c)

f(x - 5) + 3

d)

f(x - 3) + 5

136.

Which parent function matches the graph?

a)

y = |x|

b)

y = x

c)

y = x²

d)

y = 2^x

137.

What type of function is shown?

a)

absolute value

b)

quadratic

c)

linear

d)

exponential

138.

What type of function is shown?

a)

linear

b)

quadratic

c)

square root

d)

absolute value

139.

Name the parent function.

a)

linear

b)

quadratic

c)

cube root

d)

cubic

140.

Which equation below is a quadratic function translated up 5 units?

a)

y = x² + 5

b)

y = (x + 5)²

c)

y = 5x²

d)

y = -x² - 5

141.

What type of function is shown?

a)

cube root

b)

square root

c)

logarithm

d)

exponential

142.

Which equation below is a quadratic function translated left 4 units?

a)

y = x² + 4

b)

y = (x + 4)²

c)

y = (x - 4)²

d)

y = 4x²

Final Pre-College Review

Total questions: 142

Worksheet time: 7hrs 33mins

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