Free Printable KC Unit 3 Function operations and power function review

1.

f(x-2)

a)

2x² - 13x + 18

b)

2x² - 5x + 18

c)

2x² - 8x + 3

d)

2x² - 13x + 2

2.

Find f[g(5)]

a)

30

b)

242

c)

92

d)

2

3.

f(g(x))

a)

3x - 16

b)

3x - 2

c)

3x - 26

d)

4x - 2

4.

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

5.

Given that f(x) = x² + x and g(x) = 3x + 1, find the value of f(g(4)).

a)

182

b)

40

c)

61

d)

None of the Above

6.

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

a)

16

b)

4

c)

-4

d)

None of these.

7.

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

a)

19

b)

23

c)

-10

d)

None of these.

8.

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

a)

3x + 8

b)

3x - 2

c)

3x + 4

d)

None of these.

9.

g(x)=3x+4
h(x)=3x-1
Find g(h(x))

a)

-9x+11

b)

4x²+4x

c)

9x+1

d)

9x+11

10.

f(x)=x³-3x
g(x)=-4x+1
Find f(x)*g(x)

a)

-4x³-5x²-3

b)

-4x³+2x²-3x

c)

-4x⁴+x³+12x²-3x

d)

-4x^4-x³+12x²⁺3x

11.

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

12.

f(x)=2x + 4

g(x)=3x²- 1

Find f(x) ⋅ g(x)

a)

6x⁴+ 12x³- 4x²- 8x

b)

-6x³+ 12x²+ 2x - 4

c)

6x³+ 12x²- 2x - 4

d)

5x²- 18x + 20

13.

f(x)= x²- 1

g(x)= x - 1

Find (f(x)/g(x))

Then simplify using x = 10

a)

9

b)

11

c)

90

d)

110

14.

If f(x) = 2x and g(x) = 2x - 7, find f(x)/g(x).

a)

(2x - 7)/(2x)

b)

-7

c)

(2x)/(2x - 7)

d)

1x - 3.5

15.

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

16.

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)

17.

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)

18.

The inverse has been reflected over which line?

a)

y = x

b)

y =1

c)

y = 0

d)

y = x + 1

19.

Are these the graphs of two inverse functions?

a)

Yes

b)

No

c)

No way to tell

20.

When finding the inverse of a relation,
1st you replace f(x) with y
2nd switch the x's and y's
What do you do next?

a)

solve for y

b)

replace y with f^-1(x)

c)

solve for x

d)

find the greatest common factor

21.

Find the inverse of f(x) = x² - 5

a)

f^-1(x) = √(x) + 5

b)

f^-1(x) = ∛(x-5)

c)

f^-1(x) =√(x+5)

d)

f^-1(x) = x² - 5

22.

Find the inverse of
f(x) = 1/4x - 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

23.

Are the following inverses of each other?

a)

True

b)

False

24.

Find the inverse of f(x) = -3x²+5

a)

b)

c)

d)

25.

Use the horizontal line test to determine whether the inverse of the graph is a function.

a)

Function

b)

Not a Function

26.

Was the inverse function found correctly?

a)

No, should be $f^{-1}\left(x\right)$ = $\frac{\text{x-4}}{\text{3}}$

b)

Yes

27.

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

28.

What is the inverse of f(x) = $\frac{2x-6}{4}$ ?

a)

b)

c)

d)

29.

$\frac{5}{x}$ What is the restricted domain?

a)

$x\ne5$

b)

$x\ne0$

c)

$x\ge5$

d)

$x\ge0$

30.

$\frac{3}{x+4}$ What is the restricted domain?

a)

$x\ge4$

b)

$x\ge3$

c)

$x\ne3$

d)

$x\ne-4$

31.

$\frac{3}{x-6}$ What is the excluded domain?

a)

$x\ne6$

b)

$x\ne3$

c)

$x\ge3$

d)

$x\ge6$

32.

$\frac{5}{\sqrt{x-2}}$ Choose the domain for which the function is defined.

a)

$x\ne2$

b)

$x\ne5$

c)

$x\ge2$

d)

$x\ge5$

33.

$\frac{x-3}{\sqrt{x+2}}$ Choose the domain for which the function is defined.

a)

$x\ge2$

b)

$x\ge-2$

c)

$x\le2$

d)

$x\le-2$

34.

$\frac{\sqrt{x-3}}{x+8}$ Choose the domain for which the function is defined.

a)

$x\ne3\ and\ x\le8$

b)

$x\ne3\ and\ x\ge8$

c)

$x\ne8\ and\ x\ge3$

d)

$x\ne-8\ and\ x\ge3$

35.

What's the name of the inverse of g(x)?

a)

f(x)

b)

f^-1(x)

c)

y

d)

g^-1(x)

36.

Find the inverse of the function including any restriction on domain

a)

f^-1 = (x + 3)² − 4, x ≥ −3

b)

f^-1 = (x − 4)² + 3, x ≥ 4

c)

f^-1 = (x + 3)² − 4

d)

Inverse does not exist

37.

Find the inverse of the function including any restriction on domain

a)

f^-1 = (x² + 2), x ≤ 0

b)

f^-1 = (x² + 1) / 2, x ≤ 0

c)

f^-1 = (x² − 1) / 2, x ≥ 0

d)

Inverse does not exist

38.

What is the end behavior of f(x) = 3x⁶ as x goes to negative infinity?

a)

positive infinity

b)

negative infinity

c)

zero

39.

The graph most accurately represents which of the following functions?

a)

y=∛x

b)

y = x²

c)

y =x³

d)

y = 1 ∕ x

40.

Which function increases throughout

the interval -2 < x < 2?

a)

b)

c)

d)

41.

Name the interval(s) where the function is decreasing? Click all that apply.

a)

-∞ < x < -1

b)

-1 < x < 1

c)

-2 < x < 2

d)

1 < x < ∞

42.

Which statement is true about the end behavior of the function

y = -3x²?

a)

As x approaches negative infinity, y approaches 0.

b)

As x approaches positive infinity, y approaches negative infinity.

c)

As x approaches positive infinity, y approaches 0.

d)

As x approaches negative infinity, y approaches positive infinity.

43.

Describe the end behavior of the function.

a)

lim x→ ∞, f(x) = ∞
lim x → -∞, f(x) = -∞

b)

lim x→ ∞, f(x) = -∞

lim x → -∞, f(x) = -∞

c)

lim x→ ∞, f(x) = -∞

lim x → -∞, f(x) = +∞

d)

lim x→ ∞, f(x) = ∞

lim x → -∞, f(x) = ∞

44.

Which is most likely the function of the graph shown.

a)

f(x) = x^–1

b)

f(x) = ∛x

c)

f(x) = ln x

d)

f(x) = csc x

45.

Given $f\left(x-3\right)+5$ . What transformations took place from the original function f(x)?

a)

Left 3 and up 5

b)

Right 3 and down 5

c)

Left 3 and down 5

d)

Right 3 and up 5

46.

If the blue graph is f(x) (the original function) and the red graph is the transformation, what is the equation of the red graph?

a)

-f(x)

b)

f(-x)

c)

f^-1(x)

d)

f(2x)

47.

The blue function is the original function f(x) = x³. Which of the following is the correct equation for the red function, g(x)?

a)

$g\left(x\right)=x^3+1$

b)

$g\left(x\right)=x^3-1$

c)

$g\left(x\right)=\left(x-1\right)^3$

d)

$g\left(x\right)=\left(x+1\right)^3$

48.

$3f\left(x-2\right)$ Identify the transformations.

a)

horizontal shift to the left 2 and vertical stretch by a factor of 3

b)

horizontal shift to the right 2 and vertical stretch by a factor of 3

c)

horizontal shift to the right 2 and vertical shrink by a factor of 3

d)

horizontal shift to the left 2 and vertical shrink by a factor of 3

49.

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

a)

Reflect over y-axis then right 3.

b)

Reflect over y-axis then left 3.

c)

Reflect over x-axis then left 3.

d)

Reflect over x-axis then right 3.

50.

Describe the transformation of $y=f\left(x\right)$ to the new function $y=f\left(\frac{1}{5}x\right)$

a)

Horizontal compression by a factor of 1/5

b)

Vertical stretch be a factor of 5

c)

Vertically compression by a factor of 1/5

d)

Horizontal stretch by a factor of 5

51.

How is this function transformed from the parent function?

a)

Translated left

b)

Translated right

c)

Translated down

d)

Translated up

52.

How is this function transformed from the parent function?

a)

Translated left and up

b)

Translated right and up

c)

Translated left and down

d)

Translated right and down

53.

Given that $f\left(x\right)$ is an even function and that $f\left(-3\right)=19$ , which statement must also be true?

a)

$f\left(3\right)=19$

b)

$f\left(-3\right)=-19$

c)

$f\left(3\right)=-19$

d)

$f\left(19\right)=-3$

54.

$y=x^2+3x+9$

a)

Even Function

b)

Odd Function

c)

Function - neither even nor odd

d)

Not a function

55.

The function shown in the graph is:

a)

Even

b)

Odd

c)

Neither Even nor Odd

d)

Not a Function

56.

Is this function even, odd or neither?

a)

Even

b)

Odd

c)

Neither

57.

Which one of the following functions is even?

a)

f(x) = x⁴ + x³

b)

g(x) = x⁴ + x²

c)

h(x) = x⁵ + x³

d)

k(x) = x³ + x

58.

Which one of the following functions is odd?

a)

f(x) = 3x⁴ - 4x³

b)

g(x) = 5x⁴ + 3x²

c)

h(x) = 6x⁵ - x³

d)

k(x) = x⁶ + 8x²

59.

The function in the graph is:

a)

even

b)

odd

c)

neither even nor odd

d)

both even and odd

60.

The function shown in the graph is:

a)

even

b)

odd

c)

neither odd nor even

d)

both odd and even

61.

Which one means left

a)

x →-∞

b)

x →∞

62.

Which one means up

a)

y →-∞

b)

y →∞

63.

Which one means the function goes up on the left

a)

x →-∞, y→∞

b)

x →-∞, y→-∞

64.

Which one means the function goes down on the left

a)

x →-∞, y→∞

b)

x →-∞, y→-∞

65.

What is the end behavior of the function

a)

$\lim_{x\rightarrow-\infty}f\left(x\right)=+\infty\ ;\ \lim_{x\rightarrow+\infty}f\left(x\right)=+\infty$

b)

$\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty\ ;\lim_{x\rightarrow+\infty}f\left(x\right)=+\infty$

c)

$\lim_{x\rightarrow-\infty}f\left(x\right)=+\infty\ ;\lim_{x\rightarrow+\infty}f\left(x\right)=-\infty$

d)

$\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty\ ;\lim_{x\rightarrow+\infty}f\left(x\right)=-\infty$

66.

What is the end behavior of the function

a)

$\lim_{x\rightarrow-\infty}f\left(x\right)=+\infty;\ \lim_{x\rightarrow+\infty}f\left(x\right)=+\infty$

b)

$\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty\ ;\lim_{x\rightarrow+\infty}f\left(x\right)=-\infty$

c)

$\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty;\ \lim_{x\rightarrow+\infty}f\left(x\right)=+\infty$

d)

$\lim_{x\rightarrow-\infty}f\left(x\right)=+\infty;\ \lim_{x\rightarrow+\infty}f\left(x\right)=-\infty$

67.

What is the increasing interval on the function shown?

a)

$\left(-\infty,\ 1\right)$

b)

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

c)

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

d)

$\left(1,\ \infty\right)$

68.

What is the decreasing interval on the function shown?

a)

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

b)

$\left(-\infty,\ -4\right)$

c)

$\left(-4,\ \infty\right)$

d)

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

69.

What is the increasing interval on the function shown?

a)

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

b)

$\left(-\infty,\ -4\right)$

c)

$\left(-4,\ \infty\right)$

d)

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

70.

Where is the function decreasing?

a)

x≤1

b)

x≥1

c)

x≤2

d)

x≥2

71.

Where is the function decreasing?

a)

x≤0

b)

x≥0

c)

x≤1

d)

x≥1

72.

Where is the function increasing?

a)

x≤-1

b)

x≥-1

c)

x≤0

d)

x≥0

73.

Suppose a function $f\left(x\right)$ has domain $x\ge3$ and range $y\ge0$ . What is the domain of $f^{-1}\left(x\right)$ , the inverse of $f\left(x\right)$

a)

$x\le3$

b)

$y\le0$

c)

$x\ge0$

d)

$y\ge3$

74.

Which function is the inverse of $f\left(x\right)=\sqrt{x+4}$ ?

a)

$g\left(x\right)=x^2-4$

b)

$g\left(x\right)=\left(x-4\right)^2$

c)

$g\left(x\right)=\sqrt{x-4}$

d)

$g\left(x\right)=x+4$

75.

The domain of a function is All Real Numbers. What does that mean about the inverse of the function?

a)

The domain of the inverse is also All Real Numbers.

b)

The range of the inverse is All Real Numbers.

c)

The inverse must be a function.

d)

This doesn't tell me anything about the inverse.

76.

$If\ \ g\left(x\right)=\sqrt{x-5}$ what restrictions on the domain will keep the inverse a function?

a)

$x\ge5$

b)

$x\ge0$

c)

$x\ne5$

d)

$x\ge-5$

77.

$Identify\ the\ transformatins\ for\ 2\sqrt{10-5x\ \ \ }$

a)

vertical stretch of 2, horizontal reflection, horizontal compression by factor of 5 and translation right of 2.

b)

vertical stretch of 2, horizontal reflection, horizontal stretch by factor of 5 and translation left of 10.

c)

vertical stretch of 2, horizontal reflection, horizontal compression by factor of 5 and translation left of 10.

d)

vertical stretch of 5, horizontal reflection, horizontal compression by factor of 2 and translation right of 10.

78.

Which power function is always increasing?

a)

$f\left(x\right)=\left|x\right|$

b)

$g\left(x\right)=x^2$

c)

$h\left(x\right)=\frac{1}{x}$

d)

$j\left(x\right)=x^3$

79.

Can we do something so the inverse of this function will be a function?

a)

No

b)

$\left[0,\infty\right)$

Yes, you can restrict the domain.

c)

Yes, restrict the range to $y\ge-4$

d)

$Yes,\ restrict\ the\ domain\ to\ x\ge-4.$

KC Unit 3 Function operations and power function review

Total questions: 79

Worksheet time: 4hrs 34mins

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