Free Printable Section 1.9

1.

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

2.

What is the inverse of the given coordinates: (1, 2) (3, 8) (-3, 6)

a)

(1, 2) (3, 8) (-3, 6)

b)

(1, 2) (8, 3) (-3, 6)

c)

(-1, -2) (-3, -8) (3, -6)

d)

(2, 1) (8, 3) (6, -3)

3.

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

a)

1

b)

-1

c)

2

d)

-2

4.

Find the inverse
f(x)=2x-2

a)

f^-1(x)=1/2x+1

b)

f^-1(x)=-2-1/2x

c)

f^-1(x)=-7/3x-20/3

d)

2-2/5x

5.

In an inverse function, the _____ and _______ are switched from the original

a)

f(x) and g(x)

b)

input and output

c)

positives and negatives

d)

slope and intercept

6.

Given f(x) = x+3, find f^-1(-2).

a)

-1

b)

1

c)

5

d)

-5

7.

a)

9 - √17

b)

4

c)

2

d)

√8

8.

What is the inverse of this function?

a)

A

b)

B

c)

C

d)

D

9.

a)

A

b)

B

c)

C

d)

D

10.

Given f(x)= -3x+7 and g(x)=2x² - 8, find g(f(x)).

a)

g(f(x))= -6x²+31

b)

g(f(x))= -6x²+24

c)

g(f(x))=18x²-84x+90

d)

g(f(x))=9x²-42x-41

11.

Are the following inverses of each other?

a)

True

b)

False

12.

Was the inverse function found correctly?

a)

no,

b)

yes

13.

What is the inverse of this function?

a)

A

b)

B

c)

C

d)

D

14.

What is the best description?

a)

They are both functions, but not inverse functions.

b)

They are reflected over y=x, but they are not both functions.

c)

They are not reflected over y=x, and they are not both functions.

d)

They are inverse functions.

15.

What's the best description?

a)

They are both functions, but not inverse functions.

b)

They are reflected over y=x, but they are not both functions.

c)

They are not reflected over y=x, and they are not both functions.

d)

They are inverse functions.

16.

What's the best description?

a)

They are both functions, but not inverse functions.

b)

They are reflected over y=x, but they are not both functions.

c)

They are not reflected over y=x, and they are not both functions.

d)

They are inverse functions.

17.

What is the best description?

a)

They are both functions, but not inverse functions.

b)

They are inverse functions.

c)

They are reflected over y=x, but they are not both functions.

d)

They are not reflected over y=x, and they are not both functions.

18.

a)

b)

c)

d)

19.

How must the domain of f(x) be restricted such that g(x)=f^-1(x) ?

a)

x ≤ 0

b)

x ≥ 0

c)

x ≤ 3

d)

x ≥ 3

20.

How must the domain of f(x) be restricted such that g(x)=f^-1(x) ?

a)

x ≤ -4

b)

x ≥ -4

c)

x ≤ 0

d)

x ≥ 0

21.

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

a)

16

b)

4

c)

-4

d)

None of these.

22.

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

23.

Convert to vertex form.

a)

y=3(x+1)² - 8

b)

y=3(x-1)² - 8

c)

y=3(x+2)² - 8

d)

y=3(x-2)² - 8

24.

Write the equation of the quadratic in vertex form given the following:
vertex: (4, -2)
point: (0,-6)
opens down

a)

f(x)=(x-4)²-2

b)

f(x)=-4(x-4)²-2

c)

f(x)=1/4(x+4)²-2

d)

f(x)=-1/4(x-4)²-2

25.

What is the range of this function?

a)

(- ∞,+∞)

b)

[0, +∞)

c)

[-2, +∞)

d)

[2, +∞)

26.

What is the axis of symmetry for the following equation?
y=4x²-8x+9

a)

x=-8

b)

x=1

c)

x=-1

d)

x=2

27.

Which equation best represents the graph?

a)

y = 2(x - 4)² + 5

b)

y = 2(x + 4)² + 5

c)

y = -2(x - 4)² + 5

d)

y = -2(x + 4)² + 5

28.

Which answer choice describes y = -3x² +7x - 2 accurately?

a)

opens up with a maximum

b)

opens up with a minimum

c)

opens down with a maximum

d)

opens down with a minimum

29.

.How many zeros does this parabola have?

a)

3

b)

2

c)

0

d)

1

30.

Find the vertex of
f(x) = -x²- 4x + 12.

a)

(-2, 16)

b)

(2, 0)

c)

(2, 4)

d)

(-2, 4)

31.

How many solutions does this graph have?

a)

one

b)

two

c)

no solutions

d)

cannot be determined

32.

What is the equation for the axis of symmetry of
f(x)= (x +1)² + 5

a)

x = 1

b)

x = -1

c)

x = -5

d)

x = 5

33.

What is the vertex form of this quadratic?

a)

f(x) = -(x + 2)²- 4

b)

f(x) = (x - 2)²+ 4

c)

f(x) = (x - 2)²- 4

d)

f(x) = -(x - 2)² - 4

34.

How did we transform from f(x) =x²tog(x) = -3x²

a)

reflection in x-axis and vertical shift down

b)

reflection x-axis and vertical stretch

c)

horizontal stretch

d)

reflection x-axis and vertical compression

35.

Vertical line through the vertex, about which the parabola is symmetric.

a)

x-intercept

b)

Parabola

c)

y-intercept

d)

Axis of symmetry

36.

Which statement about the graph is FALSE?

a)

The vertex is also a zero of the function

b)

The y-intercept is (0, -2)

c)

The axis of symmetry is x = 2

d)

The range is y ≥ 0

37.

State the domain and range.

a)

Domain: All real numbers, Range: y ≥ -9

b)

Domain: All real numbers, Range: All real numbers

c)

Domain: x ≥ -8, Range: y ≥ -9

d)

Domain: x ≥ -8, Range: All real numbers

38.

f(x) = 2x³ - 3x² + 4x -10

What is the degree of f(x)?

a)

3

b)

2

c)

1

d)

0

39.

f(x) = 2x³ - 3x² + 4x -10

State the maximum and minimum number of zeros for f(x).

a)

Max: 3 Min: 0

b)

Max 2 Min: 0

c)

Max: 1 Min: 1

d)

Max: 3 Min: 1

40.

f(x) = -3x⁴ + x³ - 2x² + x - 1

State the maximum and minimum number of zeros for f(x).

a)

Max: 4 Min: 1

b)

Max: 3 Min: 0

c)

Max: 4 Min: 0

d)

Max: 3 Min: 1

41.

f(x) = x³ - 3x² - 4x

Find the zeros of f(x).

a)

{-4, 0, 1}

b)

{-1, 4}

c)

{-1, 0, 4}

d)

{-4, 1}

42.

f(x) = 2x³ - x² -x

Find the zeros of f(x).

a)

{-½, 1}

b)

{-1, 0, ½}

c)

{-1, 0, 2}

d)

{-½, 0, 1}

43.

f(x) = x⁴ - 7x³ + 10x²

Find the zeros of f(x).

a)

{0, 2, 5}

b)

{0, 5}

c)

{-4, 0, 2}

d)

{0, 5/3, 2}

44.

f(x) = x³ - 9x² - 45x - 27

Find the remaining zeros given that -3 is a zero of f(x).

a)

{-3, -6 ± 3√5}

b)

{-3, 6 ± 3√5}

c)

(-3, 3, 9}

d)

{-3, 0, 3}

45.

Write a polynomial function with the given zeros.

a)

A

b)

B

c)

C

d)

D

46.

Find all zeros of the polynomial function P(x) = x³+6x²+9x+54

a)

6, 3, -3

b)

-6, 3, -3

c)

-6, 3i, -3i

d)

6, 3i, -3i

47.

Find all zeros for the polynomial function P(x) = x³ -3x²-5x+15

a)

3, √5

b)

3, √5, -√5

c)

-3, √5, -√5

d)

-3, 5i, -5i

48.

Classify the function:

a)

quadratic

b)

cubic

c)

quartic

d)

linear

49.

Does this graph have an absolute minimum?

a)

Yes

b)

No

50.

How many relative extrema are in the picture?

a)

2

b)

3

c)

4

d)

5

51.

Which of the following could be the equation of this graph in factored form? (Careful-pay attention to multiplicity.)

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)

52.

Which is true about the equation of the graph shown?

a)

The function has an Odd degree

b)

The function has an Even degree

c)

The function has 5 real zeros

d)

The function has a positive leading coefficient

53.

What are the zeros of the polynomial function?

y = (x + 2)(x - 7)³

a)

-2, 7 multiplicity 3

b)

-2, 7, 3

c)

2, -7 multiplicity 3

d)

2, -7, 3

54.

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

a)

Cross the x-axis

b)

Tangent to the x-axis

55.

Which equation MOST LIKELY matches the graph?

a)

y = x⁴- x³ + 3x² + 2

b)

y = -x⁴ + x³ + 5x + 2

c)

y = x³ - 2x² + 1x + 3

d)

y = -x³ - 2x² + 1x + 3

56.

Given
$f\left(x\right)\ =\ 10x^2\left(2x-2\right)^3\left(x^2+3\right)$ ,
what is the multiplicity of $x=0$ ?

a)

10

b)

3

c)

2

d)

0

57.

Given $f\left(x\right)\ =\ \left(2x\ +6\right)^7\left(x-3\right)^4$ ,
what is the multiplicity of the root $x=-3$ ?

a)

7

b)

2

c)

6

d)

4

58.

At the root $x=1$ on $f\left(x\right)\ =\ \left(3x+3\right)^7\left(6x-6\right)^2\left(x^2+1\right)$ the graph...

a)

Bounces off of $y=0$ like a parabola

b)

Passes through $y=0$ like a line

c)

Passes through $y=0$ like a "wave"

d)

$x=1$ is not a root

59.

Which graph represents $f\left(x\right)\ =\ -3x\left(x-1\right)^2\left(x+3\right)^3$ ?

a)

b)

c)

d)

60.

Based on the end behavior which option best describes the leading term?

Remember to look at your roots, multiplicity, and end behavior!!

Use your notes!

a)

negative coefficient, even degree

b)

negative coefficient, odd degree

c)

negative degree, odd coefficient

d)

negative degree, even coefficient

61.

solve using long division

a)

2x² - x + 1 + 9/(x-2)

b)

2x³ - x² + x + 9

c)

2x² - x + 10

d)

x² - 2x + 1

62.

solve using long division

a)

x - 7

b)

x²- 7

c)

x + 7

d)

x²+ 3x - 54

63.

solve using long division

a)

x + 5 + (2/2x - 4)

b)

x - 8

c)

x - 5 + (3/2x - 4)

d)

x + 5

64.

i⁶⁶

a)

1

b)

i

c)

-1

d)

-i

65.

i¹³

a)

-1

b)

1

c)

i

d)

-i

66.

Simplify:
(3 + 2i) + (4i + 6)

a)

9 + 6i

b)

7i + 8

c)

9 + 6i²

d)

9 - 6i

67.

Simplify:
(4 + 7i) - (3 + 2i)

a)

1 + 5i

b)

7 + 9i

c)

1 + 9i

d)

-1 + 5i

68.

Simplify:
-3i(4 + 2i)

a)

6 - 12i

b)

6 + 12i

c)

-12i - 6i²

d)

-12i + 6i²

69.

Simplify:
(2 - 3i)(5 + 4i)

a)

22 - 7i

b)

22 + 7i

c)

22 - 7i²

d)

22 + 7i²

70.

What is the complex conjugate of 4-3i?

a)

A. 1/(4-3i)

b)

B. 1/(4+3i)

c)

C. -4 + 3i

d)

D. 4 + 3i

71.

(4-5i)(4+5i)

a)

41

b)

-9

c)

41+40i

d)

-9+40i

72.

a)

A

b)

B

c)

C

d)

D

73.

(-7+6i)²

a)

49+36i

b)

85

c)

13-84i

d)

13+84i

74.

Simplify

a)

(-10+6i)/17

b)

(1+50i)/61

c)

(-23+36i)/25

d)

(-21+33i)/34

75.

a)

A

b)

B

c)

C

d)

D

76.

Solve for x:

a)

x = {-3+2i, -3-2i}

b)

x = {7, 6}

c)

x = 2±i√3

d)

No solution

77.

Find the roots: x² - 8x - 20 = 0

a)

x = {10, -2}

b)

x = {-10, 2}

c)

x = (8±√12)/2

d)

x = {6, 1}

78.

Solve for x: x² - 5x + 8 = 0

a)

x = (-5±i√7)/2

b)

x = (5±i√7)/2

c)

x = (8±i√7)/2

d)

x = (5±√57)/2

79.

what is the equation that best matches the graph?

a)

A

b)

B

c)

C

d)

D

80.

What is/are the vertical asymptote(s)?

a)

There are no vertical asymptotes

b)

x=5

c)

x=-5

d)

x=-1/2

81.

What are the Vertical Asymptotes of...

a)

x = 0, -5

b)

x=0, 5

c)

x = 2, -7

d)

x = -2, 7

82.

What is the Horizontal Asymptote?

a)

None

b)

y= 0

c)

y= 1

d)

y= 5/4

83.

What is the hole?

a)

x= 4

b)

x= -4

c)

x= 5

d)

x= -5

84.

Find the horizontal asymptote.

a)

None

b)

y = 0

c)

y = -1/3

d)

y = -3

85.

What is/are the x-intercepts of this graph?

a)

(-2,0) and (2,0)

b)

(-2,0)

c)

(3,0)

d)

(2,0) and (3,0

86.

Which of the following could be a possible equation for the function shown?

a)

f(x) =-2x³ + x² - 5x + 1

b)

f(x) = 2x³ - 4x² + x + 1

c)

f(x) = 3x² + 5x + 1

d)

f(x) = -2x³ +3x - 1

87.

State the minimum degree of the function shown:

a)

3

b)

4

c)

5

d)

6

88.

Select all the graphs which show even degree functions.

a)

b)

c)

d)

89.

Which of the following functions could represent the graph shown?

a)

f(x) = -2x⁵

b)

f(x) = -2x⁴ + 7x³ + 3x² -5x + 8

c)

f(x) = 2x⁵ + 3x⁴ - 3x³ + 5x² - 3x + 4

d)

None of these functions could represent the graph shown.

90.

Which description best matches the function shown:

a)

Odd degree with positive leading coefficient.

b)

Even degree with positive leading coefficient.

c)

Degree three, with negative leading coefficient.

d)

Degree four, with negative leading coefficient.

91.

Select all the even degree functions.

a)

A

b)

B

c)

C

d)

D

92.

a)

y = ^_(x + 2)(x - 1)²

b)

y = -(x - 2)(x + 1)²

c)

y = (x - 2)(x + 1)²

d)

y = -x³

93.

a)

f(x) = (x − 1)²(x + 2)(x + 4)³

b)

f(x) = (x + 1)(x − 2)(x − 4)

c)

f(x) = (x + 1)²(x − 2)(x − 4)³

d)

f(x) = (x + 1)(x − 2)(x − 4)³

94.

What's the horizontal asymptote of the function?

a)

y = 0

b)

No horizontal asymptote

c)

y = 1/2

d)

y = 1

95.

What's the vertical asymptote of the function?

a)

x = 5

b)

x = 0

c)

x =5 , x = -5

d)

x = 25

96.

Where is the removable discontinuity?

a)

x=2

b)

x=2 and x=3

c)

x=-3

d)

x=3

Section 1.9 - 2.6 Review

Total questions: 96

Worksheet time: 5hrs 56mins

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