Free Printable Fall 2023 Final Exam Review Part 1: Functions

1.

What is the y-coordinate for the point of inflection of the function:

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

2.

What is the x-coordinate for the point of inflection of the function:

$f\left(x\right)=3\left(x+6\right)^3$

3.

What are the relative maximums for this graph?

a)

{2.2, 3.9}

b)

{-8, 5}

c)

{3.9, 5}

d)

{-8, 2.2}

4.

What is the absolute min?

a)

0

b)

-6.55

c)

36

d)

None

e)

$-\infty$

5.

The blue dot on this graph represents a(n)...

a)

Absolute Maximum

b)

Absolute Minimum

c)

Relative Maximum

d)

Relative Minimum

6.

What are the relative minimums for this graph? (Select all that apply)

a)

$-\infty$

b)

$\infty$

c)

-2.5

d)

-3.3

e)

5

7.

What is the y intercept of the function?

a)

3

b)

4

c)

-2

d)

2

8.

What are the zeros of the function? (select all that apply)

a)

-1

b)

4

c)

2.25

d)

2

e)

-2

9.

What is the range of ALL cubic functions expressed as an inequality?

a)

[-∞, ∞]

b)

(-∞,∞)

c)

-∞≤y≤∞

d)

-∞<y< ∞

10.

Describe the transformation of the graph y = -2(x + 5)³

a)

Vertical compression by 2, Reflected over y-axis, Right 5

b)

Vertical stretch by 2, Reflected over x-axis, Left 5

c)

Vertical stretch by 2, Reflected over x-axis, Right 5

d)

Vertical compression by 2, reflected over y-axis, Left 5

11.

What transformations has the function undergone?

a)

reflect over y, vertical compress by 2, right 5, up 1

b)

reflect over x, horizontal compression by 2, left 5, up 1

c)

reflect over x, vertical stretch by 2, right 5, up 1

d)

reflect over y, horizontal stretch by -2, right 5, up 1

12.

What is the point of inflection for the following cubic function?

a)

(-3, -1)

b)

(0, -4)

c)

(-1, -3)

d)

(0, 0)

13.

The graph of a function is shown. What are the domain and range of this function?

a)

Domain: (-∞, ∞)
Range: (-∞, 2]

b)

Domain: [2, ∞)
Range: (-∞, ∞)

c)

Domain: (-∞, ∞)
Range: (-∞, ∞)

d)

Domain: (-∞, 2]
Range: [2, ∞)

14.

What is f(x) =x³ symmetrical about?

a)

x axis

b)

y = x

c)

origin

d)

none

15.

If f(x) = x³ is changed to f(x) = - (x + 3)³ + 2, how is the graph transformed?

a)

3 units right, 2 units up, reflected across the y-axis

b)

3 units right, 2 units up, reflected across the x-axis

c)

3 units left, 2 units up, reflected across the y-axis

d)

3 units left, 2 units up, reflected across the x-axis

16.

What is the relative max of this function??

a)

-3.333

b)

1.185

c)

-2

d)

0

17.

What is the relative min of this function??

a)

-3.333

b)

1.185

c)

-2

d)

0

18.

How many x-intercepts does the cubic function shown have?

a)

0

b)

2

c)

3

d)

1

19.

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

a)

Even Function

b)

Odd Function

c)

Function - neither even nor odd

d)

Not a function

20.

$y=7x^8-9x^2+33$

a)

Even Function

b)

Odd Function

c)

Function - neither even nor odd

d)

Not a function

21.

$y=12x^7+6x^5-8x^3+4x$

a)

Even Function

b)

Odd Function

c)

Function - neither even nor odd

d)

Not a function

22.

The function shown in the graph is:

a)

Even

b)

Odd

c)

Neither Even nor Odd

d)

Not a Function

23.

Is this function even, odd or neither?

a)

Even

b)

Odd

c)

Neither

24.

How many extrema (maxes and mins) are in the picture?

a)

2

b)

3

c)

4

d)

5

25.

What is the relative max of this function?

a)

x = 5

b)

infinity

c)

there is no relative maximum

d)

2.5 and it occurs at x = 5

26.

What is the RANGE of this square root function?

a)

all real numbers

b)

$x\ge0$

c)

$y\le0$

d)

$y\ge-3$

27.

What is the DOMAIN of this square root function?

a)

all real numbers

b)

$x\ge1$

c)

$x\le1$

d)

$x\ge2$

28.

What is the X-INTERCEPT of this square root function?

a)

(0,0)

b)

(9,0)

c)

(0,-3)

d)

(1,1)

29.

What is the Y-INTERCEPT of this square root function?

a)

(0,0)

b)

(9,0)

c)

(0,-3)

d)

(1,1)

30.

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

31.

When finding the inverse of the radical function; $f(x)=4\sqrt[3]{x-5}$ , you must first

a)

cube both sides

b)

square both sides

c)

divide by 4

d)

switch x & y

e)

add 5

32.

The first step in finding the inverse to the function $f(x)=\frac{\left(x-5\right)\left(x+5\right)}{\left(x-4\right)\left(x+3\right)}$ is to...

a)

multiply by the denominator

b)

cancel out matching factors

c)

perform all transformations

d)

switch x & y

e)

find all the coordinates for the graph

33.

Find the inverse of f(x) = -3x²+5

a)

b)

c)

d)

34.

Select the table that represents the inverse of this relation:

a)

b)

c)

d)

35.

What is the domain for:

g(x) = √(x + 5) - 3

a)

A

-3 ≤ x < ∞

b)

B

− ∞ < x ≤ -3

c)

C

-5 ≤ x < ∞

d)

D

− ∞ < x ≤ -5

36.

$f(x)=-2-\sqrt[]{-2x}$

a)

Reflect over x-axis

Reflect over y-axis Down 2

Horizontal compression by 2

b)

Reflect over x-axis

Reflect over y-axis Up 2

Vertical compression by 2

c)

Reflect over x-axis

Down 2

Horizontal stretch by 2

d)

Reflect over y-axis Up 2

Horizontal compression by 2

37.

Which function matches the graph?

a)

$f\left(x\right)=-2+\sqrt[]{x-4}$

b)

$f\left(x\right)=2+\sqrt[]{x-4}$

c)

$f\left(x\right)=-4+\sqrt[]{x-2}$

d)

$f\left(x\right)=-2+\sqrt[]{x+4}$

38.

What is the equation of the graph?

a)

$f\left(x\right)=\sqrt[]{-x+3}$

b)

$f\left(x\right)=3+\sqrt[]{-x}$

c)

$f\left(x\right)=\sqrt[]{x+3}$

d)

$f\left(x\right)=3-\sqrt[]{x}$

39.

What is the Range for the graph?

a)

2 ≤ y < ∞

b)

− ∞ < y ≤ 3

c)

3 ≤ y < ∞

d)

− ∞ < y < ∞

40.

If f(x) = ∛(x) is reflected over the x-axis, vertically compressed by a factor of 1/4, and shifted left 9, which equation is correct?

a)

1/4 ∛(x + 9)

b)

1/4 ∛(x - 9)

c)

- 1/4 ∛(x + 9)

d)

- 1/4 ∛(x - 9)

41.

Which function matches the graph?

a)

$f\left(x\right)=2+\sqrt[3]{x+3}$

b)

$f\left(x\right)=2-\sqrt[3]{x+3}$

c)

$f\left(x\right)=2+\sqrt[3]{x-3}$

d)

$f\left(x\right)=3+\sqrt[3]{x-2}$

42.

Which function matches the graph?

a)

$f\left(x\right)=-1+\sqrt[3]{x+3}$

b)

$f\left(x\right)=-1-\sqrt[3]{x-3}$

c)

$f\left(x\right)=-1-\sqrt[3]{x+3}$

d)

$f\left(x\right)=3+\sqrt[3]{x-1}$

43.

What transformations have occurred to get from the parent function f(x) to the transformed function g(x)?

a)

reflection over the x-axis,vertical shrink by a factor of -5

b)

reflection over the x-axis,vertical shrink by a factor of 1/5

c)

reflection over the x-axis,vertical stretch by a factor of 5

d)

reflection over the y-axis,vertical stretch by a factor of 5

44.

If f(x) = ∛(x) is reflected over the x-axis, vertically shrunk by a factor of 1/4, and shifted left 9, which equation is correct?

a)

1/4 ∛(x + 9)

b)

1/4 ∛(x - 9)

c)

- 1/4 ∛(x + 9)

d)

- 1/4 ∛(x - 9)

45.

What is the horizontal asymptote for

f\left(x\right)=\frac{-3}{x}+2

a)

x = -3

b)

x = 0

c)

y = 2

d)

y = -2

46.

What is the vertical asymptote for

f\left(x\right)=\frac{1}{x+4}-5

a)

x = -4

b)

x = 4

c)

y = 5

d)

y = -5

47.

What information would help you determine the vertical asymptote? (Check all that apply)

a)

The value of x that makes the denominator equal to zero

b)

The "h" value

c)

The "k" value

d)

The range

e)

The domain

48.

What is the domain of

f\left(x\right)=\frac{-1}{x-2}-4

a)

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

b)

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

c)

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

d)

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

49.

What is the range of

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

a)

$\left(-\infty,\ 0\right)\cup\left(0,\ \infty\right)$

b)

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

c)

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

d)

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

50.

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

51.

Write the equation for the graph.

a)

$y=\frac{1}{x-1}-2$

b)

$y=\frac{1}{x+1}+2$

c)

$y=\frac{1}{x+1}-2$

d)

$y=\frac{1}{x-2}+1$

52.

Write the equation for the graph.

a)

$y=\frac{1}{x+2}+1$

b)

$y=\frac{1}{x+2}-1$

c)

$y=\frac{1}{x-2}+1$

d)

$y=\frac{1}{x-2}-1$

53.

a)

TRUE

b)

FALSE

54.

Fill in the blank

(a)

55.

In order to find a slant asymptote, you must

a)

Multiply the numerator and denominator

b)

Divide the denominator by the numerator

c)

Divide the numerator by the denominator

d)

Subtract the numerator from the denominator

56.

What are the asymptotes?

a)

x=1, x= 2, y =1, y= 2

b)

x= 2, x=-2, y = 1

c)

x=2 y =-1

d)

x=1 y =2, y =-2

57.

What is the X-Intercept?

a)

x= 0

b)

x= 4

c)

x= 5

d)

x= -5

58.

What is the horizontal asymptote of the function given?

a)

y = 2

b)

x = 1

c)

x = 2

d)

y = -1

59.

What is the horizontal asymptote to this function?

a)

y=4

b)

y=0

c)

y=-2

d)

y=1

60.

Where is the removable discontinuity/point of discontinuity?

a)

x=2

b)

x=2 and x=3

c)

x=-3

d)

x=3

61.

What is/are the vertical asymptote(s)?

a)

x=-2

b)

x=2 and x=3

c)

x=-3

d)

x=3

62.

What is the horizontal asymptote?

a)

y = -4

b)

y = 1

c)

x = 1

d)

y = -6

63.

What is the horizontal asymptote of this function?

a)

y=2

b)

x=1/2

c)

y=1

d)

y=1/2

64.

What is the Vertical Asymptotes?

a)

x= -5

b)

x= 5

c)

x= 6

d)

x= -6

65.

What are the Vertical Asymptotes of...

a)

x = 0, -5

b)

x=0, 5

c)

x = 2, -7

d)

x = -2, 7

66.

What is the Horizontal Asymptote?

a)

None

b)

y= 0

c)

y= 1

d)

y= 5/4

67.

Which asymptote(s) are determined by looking at the denominator?

a)

vertical

b)

horizontal

c)

slant

d)

none

68.

What creates a hole in the graph of a rational function?

a)

Crossing the x-axis

b)

An absence of dirt.

c)

Crossing a vertical asymptote.

d)

A factor that cancels out.

69.

What is the domain and range?

a)

D : All real number x ≠ -3
R: All real number y≠ 1

b)

D : All real number x ≠ 1
R: All real number y≠ -3

c)

D : All real number x ≠ 3
R: All real number y≠ 1

d)

D : All real number x ≠ -1
R: All real number y≠ 3

70.

What is the Domain & Range of the function

a)

D: (-∞, 5) (5,∞)

R: (-∞,1) (1,∞)

b)

D: (-∞,1) (1,∞)

R: (-∞, 5) (5,∞)

c)

D: (-∞,-1) (-1,∞)

R: (-∞,-5) (-5,∞)

Fall 2023 Final Exam Review Part 1: Functions

Total questions: 70

Worksheet time: 2hrs 59mins

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