Free Printable Precalculus Fall 2023 Final

1.

Find the distance.

a)

7.1

b)

7.8

c)

8.7

d)

8.9

2.

Find the distance between (-4, 5) and (7, 18).

a)

15.96

b)

16.08

c)

16.23

d)

17.03

3.

Find the distance between J and K.

a)

8.2

b)

7.7

c)

9

d)

10.2

4.

Solve for x:

x + 2 = 9

a)

7

b)

5

c)

9

d)

11

5.

297=7(8x-6)+3

a)

13

b)

12

c)

6

d)

10

6.

-119=1-6(3n-4)

a)

11

b)

8

c)

14

d)

9

7.

After paying $8.24 for a sandwich,Amanda has $7.71. With how much money did she start?

a)

$17.55

b)

$24.19

c)

$15.95

d)

$0.50

8.

13= r/9 + 8

a)

45

b)

5

c)

17

d)

15

9.

Seven less than 3 times a number is 18. What is the equation?

a)

3x-7 =18

b)

7+3/x=18

c)

7-3x=18

d)

x/3-7=18

10.

Henry works at Panera Bread. He deposited his paycheck of $458 into his checking account. His new total in his checking account is $2437. How much money did Henry have in his checking account before he deposited his paycheck?

a)

1979

b)

2437

c)

1854

d)

253

11.

Sam owns four times as many marbles as Jenny. Ed owns twice as many marbles as Jenny. There are a total of 63 marbles. How many marbles does Jenny own?

a)

9

b)

3

c)

6

d)

14

12.

A t-shirt printing company charges a $15 set up fee and $7 per t-shirt. If a sports team spent $169, how many t-shirts did they order?

a)

22

b)

14

c)

27

d)

11

13.

This letter represents slope

a)

y

b)

m

c)

x

d)

b

14.

This letter represents the y-intercept

a)

y

b)

m

c)

x

d)

b

15.

Which of the following is the slope-intercept form?

a)

m=yx+b

b)

2x + 3y = 25

c)

y=mx

d)

y=mx+b

16.

What type of slope is this graph?

a)

no slope

b)

undefined slope

c)

positive slope

d)

negative slope

17.

What is the y-intercept of this graphed line?

a)

7

b)

-1.5

c)

1.5

d)

2

18.

What type of slope is this graphed line?

a)

zero slope

b)

no slope

c)

negative slope

d)

positive slope

19.

What type of slope is this horizontal line?

a)

zero slope

b)

no slope

c)

positive slope

d)

negative slope

20.

Which equation below describes this graphed line?

a)

y = 4/5 x + 3

b)

y = -4/5 x - 3

c)

y = 4/5 x + 3

d)

y = -4/5 x + 3

21.

What is the slope of this data table?

a)

m = -3

b)

m = 1/3

c)

m = 3

d)

m= -1/3

22.

What is the y-intercept of this table of data?

a)

b = -4

b)

b = 4

c)

b = -6

d)

b = 6

23.

Which of the following are expressions of slope? (Choose ALL that apply).

a)

m

b)

rise/run

c)

change in y/change in x

d)

unit rate

e)

y-intercept

24.

a)

(x+1)² + (y +1)² = 3

b)

(x+1)² + (y -1)² = 3

c)

(x+1)² + (y +1)² = 9

d)

(x-1)² + (y -1)² = 9

25.

Write the equation of a circle with center (7, 0) with radius 3.

a)

(x - 7)² + y² = 9

b)

x² + (y -7)² = 9

c)

(x - 7)² + y² = 3

d)

x² + (y -7)² = 3

26.

In the equation (x+2)²+(y-3)²=4, the radius of the circle is...

a)

4

b)

2

c)

3

d)

16

27.

What are the coordinates of the center and the radius of the circle with an equation:
(x + 7)² + (y - 6)² = 64 ?

a)

Centre (7,-6)
Radius = 8 units

b)

Centre (-7,6)
Radius = 64 units

c)

Centre (-7,6)
Radius = 8 units

d)

Centre (7,-6)
Radius = 64 units

28.

Which graph corresponds to
(x-8)²+ (y+2)²=

a)

A

b)

B

c)

C

d)

D

29.

In the circle represented by the equation (x-4)²+(y-3)²=25, the diameter is

a)

10

b)

3

c)

5

d)

25

30.

In the equation (x+2)²+(y-3)²=4, the diameter of the circle is...

a)

4

b)

2

c)

3

d)

16

31.

The middle of a line is called the _______________.

a)

endpoint

b)

midpoint

c)

slope

d)

distance

32.

What formula would I use to find the x-coordinate of the midpoint between (3,9) and (5,9)

a)

$\frac{3+5}{2}$

b)

$\frac{3+9}{2}$

c)

$\frac{5+9}{2}$

d)

$\frac{9+9}{2}$

33.

What formula would I use to find the y-coordinate of the midpoint between (3,9) and (5,9)

a)

$\frac{3+5}{2}$

b)

$\frac{3+9}{2}$

c)

$\frac{5+9}{2}$

d)

$\frac{9+9}{2}$

34.

What is the x-coordinate of the midpoint between (-4,4) and (-2,2)?

a)

3

b)

-3

c)

4

d)

6

35.

What is the y-coordinate of the midpoint between (-4,4) and (-2,2)?

a)

3

b)

-3

c)

4

d)

6

36.

Find the midpoint of the line segment with the given endpoints (1,1) and (9,9)

a)

(5,5)

b)

(1,9)

c)

(17,17)

d)

(-4,-4)

37.

Find the midpoint: $\left(2,-7\right),\left(10,1\right)$

a)

(-3,6)

b)

(6,-3)

c)

(4,4)

d)

none

38.

Slopes of parallel lines are...

a)

opposite reciprocals.

b)

opposites.

c)

the same.

d)

always 7.

39.

Slopes of perpendicular lines are...

a)

opposite reciprocals.

b)

opposites.

c)

the same.

d)

always 7.

40.

y = -2/3x + 2
y = 3/2x + 9
These lines are...

a)

Parallel

b)

Perpendicular

c)

Neither

41.

What slope is perpendicular to:
m = 5/8

a)

-5/8

b)

5/8

c)

-8/5

d)

8/5

42.

y = 6x + 2
y = -6x + 2
These lines are...

a)

Parallel

b)

Perpendicular

c)

Neither

43.

y = 3x +2
y = 3x - 3
These lines are...

a)

Parallel

b)

Perpendicular

c)

Neither

d)

The same line

44.

Match the following

a)

1.

Parallel lines

b)

2.

Perpendicular lines

c)

3.

Intersecting lines

45.

Match the following opposite reciprocal

a)

-2/3

1.

3/2

b)

5/4

2.

-4/5

c)

15/4

3.

-4/15

d)

-7/5

4.

5/7

46.

Two lines that are perpendicular lines have ...

a)

Slopes that are negative reciprocals

b)

No Slope

c)

Slopes that are the same

d)

Slopes that switch the numbers

47.

What is the slope of a line parallel to the line

y=-5x-17

a)

$\frac{1}{5}$

b)

-5

c)

$-\frac{1}{5}$

d)

5

48.

What is the slope of a line perpendicular to:

y=13x-2

?

a)

$\frac{1}{13}$

b)

$-\frac{1}{13}$

c)

13

d)

-13

49.

What is the domain of this graph?

a)

{-2 ≤ x ≤ 4}

b)

{-5 ≤ x ≤ 4}

c)

{-4, 0, -2}

d)

{-4 ≤ x ≤ 2}

50.

What is the domain of this graph?

a)

All Real Numbers

b)

x ≥ -2

c)

x < 6

d)

-2 < x < 6

e)

x ≤ -2

51.

Parabolas go up forever. What is the range?

a)

y ≥ -2

b)

y ≥ 0

c)

y < 5

d)

y < 2

e)

y > 0

52.

What is the range of this graph?

a)

y < 3

b)

y > -3

c)

y ≥ 0

d)

All Real Numbers

53.

What is the domain of a relation?

a)

the set of all x-values

b)

the set of all y-values

54.

What is the RANGE of this graph?

a)

-7 < x < 5

b)

-7 ≤ y < 5

c)

-3 < x < 1

d)

-3 ≤ y < 1

55.

What is the Domain?

a)

y ≥ 6

b)

All real numbers

c)

-10 ≤ y ≤ 6

d)

-10 ≤ x ≤ 6

56.

All of the y values or outputs are called what?

a)

Domain

b)

Range

57.

Before a bowler rolls her first ball, 10 pins are standing. The number of pins that will be left standing, y, is a function of the number of pins she knocks down. What is the range of the function?

a)

{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

b)

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

c)

y ≤ 10

d)

0 ≤ y ≤ 10

58.

What is the range of the table?

a)

{-4, 0, 1, 3}

b)

{-2, 0, 2, 3}

c)

{-4, -2, 0, 1, 2, 3}

d)

{ (0, 0), (2, -4), (3, 3), (-2, 1) }

59.

What is the domain of the relation shown in the table?

a)

{12}

b)

{6, 18}

c)

{3, 9, 15, 16}

d)

{13}

60.

What is the range of the following relation:
(9, -2) (4, 3) ( 8, 10) ( -4, 8)

a)

{-4, 4, 8, 9}

b)

{-2, 3, 8, 10}

c)

{(9, -2) ( 4, 3)}

d)

{(8, 10) (-4, 8)}

61.

What is the range?

a)

{-3, -1, 2, 4}

b)

{0, 4, 7}

c)

{0, 4, 4, 7}

d)

{7, 4, 0}

62.

Is the relation a function? Why.

a)

Yes, because the x-value 11 has two y-values pair with it.

b)

Yes, because each x-value has only one y-value paired with it.

c)

No, because the x-value 11 has two y-values pair with it.

d)

No, because each x-value has only one y-value paired with it.

63.

a)

It is a Function

b)

Not a Function

64.

a)

It is a Function

b)

Not a Function

65.

a)

It is a Function

b)

Not a Function

66.

a)

It is a Function

b)

Not a Function

67.

a)

It is a Function

b)

Not a Function

68.

a)

It is a Function

b)

Not a Function

69.

a)

It is a Function

b)

Not a Function

70.

Does this graph have a maximum or minimum value?

a)

maximum

b)

minimum

c)

neither

d)

both

71.

What are the x-intercepts of the graph?

a)

(2, 0)

b)

(0, -2)

c)

(-1.225, -4.25) and (1.225, -4.25)

d)

(-1.887, 0) and (1.887, 0)

72.

What is the y-intercept of the graph?

a)

(-2,5)

b)

(1,0)

c)

(0,1)

d)

(-3.104, 0)

73.

What is the minimum of the graph?

a)

(0,5)

b)

(-5, 0) (1, 0)

c)

(-2, 9)

d)

It does not have one

74.

What best describes the increasing/decreasing of the graph?

a)

decreasing, increasing

b)

decreasing, increasing, decreasing

c)

increasing, decreasing, increasing

d)

increasing, decreasing

75.

When is the function decreasing?

a)

(30, 55)

b)

(40, 60]

c)

(15, 40)

d)

(60, -40)

76.

What is the interval of increase?

a)

( - $\infty$ , -2)

b)

(-2, $\infty$ )

c)

( - $\infty$ , -3)

d)

(-3, $\infty$ )

77.

If f(x) = 3x + 8, find f(-6).

(a)

78.

If f(x) = x² + 4x - 7, find f(-3).

(a)

79.

What is the interval of decrease for this function?

(assume the graph continues past the edge)

a)

(-5, 3)

b)

(-∞,+∞)

c)

[-2, 6]

d)

\left(-2,\infty\right)

80.

What is the increasing interval for the function below?

a)

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

b)

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

c)

$\left(-\infty,6\right]$

d)

$\left(-6,6\right)$

81.

Where is the function decreasing?

a)

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

b)

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

c)

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

d)

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

82.

What is the extrema for this function?

a)

Max; (-2,-1)

b)

Min; (-2,-1)

c)

Max; (-2,1)

d)

Min; (-2,1)

83.

What is the extrema for this function?

a)

Max; (-1,4)

b)

Min; (-1,4)

c)

Max; (0,3)

d)

Min; (0,3)

84.

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

85.

Describe the transformation that occurred.

w(x) = f(x - 7)

a)

Down 7

b)

up 7

c)

right 7

d)

vertical compression

86.

Describe the transformation that occurred

m(x) = f(x + 1)

a)

left 1

b)

right 1

c)

vertical stretch

d)

up 1

87.

Describe the transformation that occurred

k(x) = f(x) - 9

a)

vertical compression

b)

down 9

c)

left 9

d)

right 9

88.

Describe the transformation that occurred

t(x) = f(x) - 1

a)

right 1

b)

down 1

c)

vertical compression

d)

vertical stretch

89.

Given f(x) = (x-3)² + 5. What transformations took place from the original function f(x)?

a)

Left 3 up 5

b)

Right 3 down 5

c)

Left 3 down 5

d)

Right 3 up 5

90.

Q.

Name the parent function.

a)

Linear

b)

quadratic

c)

cubic

d)

logarithmic

91.

Describe the transformations of f(x) when compared to the parent function. f(x)=(x+7)²

a)

horizontal shift left 7 units

b)

horizontal shift right 7 units

c)

vertical shift up 7 units

d)

vertical shift down 7 units

92.

Match the equation to its description.

a)

Right 2 and up 2

b)

Left 2 and up 2

c)

Right 2 and down 2

d)

Left 2 and down 2

93.

Which of the following transformations are present (select all that apply)?

g(x)= -2f(2(x - 1)) + 2

a)

reflection over horizontal axis

b)

reflection over vertical axis

c)

horizontal compression

d)

vertical shift

e)

Rotation about origin

94.

Describe the transformation of the equation below from the absolute value parent function. SELECT ALL THAT APPLY $g\left(x\right)=\frac{1}{2}f\left(x+3\right)-2$

a)

right 3

b)

left 3

c)

Down 2

d)

Shrink by 1/2

e)

stretch by 2

95.

The function $f\left(x\right)$ was reflected over the x-axis and vertically stretched with a scale factor of 3 and shifted 8 units up. Which rule describes this transformation?

a)

$g\left(x\right)=f\left(-3x\right)+8$

b)

$g\left(x\right)=3f\left(-x\right)+8$

c)

$g\left(x\right)=-3f\left(x-8\right)$

d)

$g\left(x\right)=-3f\left(x\right)+8$

96.

Describe the transformations that maps f(x) to g(x) = - f(x + 6) - 10

a)

Reflect over y-axis
Shifted down 10 units
Shifted left 6 units

b)

Reflect over x-axis
Shifted up 10 units
Shifted left 6 units

c)

Reflect over y-axis
Shifted up 10 units
Shifted right 6 units

d)

Reflect over x-axis
Shifted down 10 units
Shifted left 6 units

97.

If the blue is f(x),then the red must be

a)

g(x)=f(x)-5

b)

g(x)=f(x)+5

c)

g(x)=f(x-5)

d)

g(x)=f(x+5)

98.

Describe the transformation from dotted to solid.

a)

g(x) = f(x + 4)

b)

g(x) = f(x - 4)

c)

g(x) = f(x) + 4

d)

g(x) = f(x) - 4

99.

If the blue graph is f(x),the red must be...

a)

g(x) = f(x + 3)

b)

g(x) = f(x - 3)

c)

g(x) = f(x)+ 3

d)

g(x) = f(x)- 2

100.

What steps transform the graph $f\left(x\right)$ to $g\left(x\right)=-\frac{1}{2}f\left(x-4\right)+1$ ?

a)

Compressed by 1/2, shifted 4 units right and 1 unit up

b)

Reflected across x-axis, compressed by 1/2, shifted 4 units right and 1 unit up

c)

Reflected across x-axis, stretched by 1/2, shifted 4 units left and 1 unit up

d)

Stretched by 1/2, shifted 4 units right and 1 unit down

101.

Describe the transformation that occurred

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

a)

Up 5 Units

b)

vertical compression

c)

vertical stretch

d)

Down 5 Units

102.

Describe the transformation that occurred

g(x) =2f(x)

a)

Up 2 units

b)

vertical compression

c)

vertical stretch

d)

Right 2 Units

103.

What are the asymptotes for the following rational function?

$f\left(x\right)\ =\ \frac{6x}{2x+1}$ ?

a)

$y\ =3,\ x\ =\ \frac{1}{2}$

b)

$y=-\frac{1}{2},\ x\ =\ 3$

c)

$y\ =3,\ x\ =-\frac{1}{2}$

d)

$y=\frac{1}{2},\ x\ =\ 3$ y=1/2

104.

Find the Vertical Asymptotes for the following function

g\left(x\right)\ =\frac{2x^2+x-9}{x^2-2x-8}

a)

$x=-4,\ x=2$

b)

$x=-2,\ x=4$

c)

$x=-6,\ x\ =\ -2$

d)

$x=\ 2,\ x=6$

105.

What is the horizontal asymptote of the following function?

f\left(x\right)=\frac{3x^2}{4x^2-1}

a)

$y=\frac{3}{4}$

b)

$y=\frac{4}{3}$

c)

$y=0$

d)

No asymptote

106.

What is the horizontal asymptote for the following function?

f\left(x\right)=\frac{4x+3}{x^2-4}

a)

$y=4$

b)

$y=\frac{1}{4}$

c)

$y=0$

d)

No Asymptote

107.

What is the horizontal asymptote for the following function?

f\left(x\right)=\frac{5x^3+6}{x^2-9x+19}

a)

$y=5$

b)

$y=\frac{1}{5}$

c)

$y=0$

d)

No Asymptotes

108.

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

109.

What are the asymptotes?

a)

x = -2 and y = -1

b)

x = -2 and y = 1

c)

x = 2 and y = 1

d)

x = 2 and y = -1

110.

Find the vertical asymptotes and holes of the function.

a)

Holes: None;

VA: x = 1, -3

b)

Holes: x = -3;

VA: x = 1

c)

Holes: x = -3, 1

VA: None

d)

Holes: x = 1

VA: x = -3

111.

Find the horizontal asymptote.

a)

None

b)

y = 0

c)

y = -1/3

d)

y = -3

112.

What is the hole?

a)

x= 4

b)

x= -4

c)

x= 5

d)

x= -5

113.

What's the vertical asymptote of the function?

a)

x = 5

b)

x = 0

c)

x =5 , x = -5

d)

x = 25

114.

What's the vertical asymptote of the function?

a)

x = -9

b)

x = 9

c)

x = 3 , x = -3

d)

x = 3

115.

Which of the following represent(s) the domain of the function shown?

a)

x $\ne$ -3

b)

x $\ne$ 3

c)

(- $\infty$ ,3) $\cup$ (3, $\infty$ )

d)

(- $\infty$ ,-3) $\cup$ (-3, $\infty$ )

e)

(- $\infty$ ,3] $\cup$ [3, $\infty$ )

116.

What are the vertical and horizontal asymptotes of the following function?

a)

horizontal asymptote is -2 and vertical asymptote is 2

b)

horizontal asymptote is 2 and vertical asymptote is -2

c)

horizontal asymptote is -6 and vertical asymptote is 2

d)

horizontal asymptote is 1/2 and vertical asymptote is -6

e)

horizontal asymptote is 2 and vertical asymptote is -1/2

117.

What is the domain and range for the following rational function?

a)

Domain: All real numbers except -1

Range: All real numbers except 2/3

b)

Domain: All real numbers except -1

Range: All real numbers except -3/2

c)

Domain: All real numbers except 2/3

Range: All real numbers except -1

d)

Domain: All real numbers except -2/3

Range: All real numbers except -1

e)

Domain: All real numbers except 4/3

Range: All real numbers except 1

118.

green

a)

Acromiotrapezius

b)

Clavotrapezius

c)

Biceps Femoris

d)

Sartorius

119.

purple

a)

Triceps Brachii

b)

Gastrocnemius

c)

Acromiotrapezius

d)

Levator Scapula

120.

Red

a)

Latissimus Dorsi

b)

External Oblique

c)

Spinotrapezius

d)

Sartoris

121.

Yellow

a)

Latissimus Dorsi

b)

External Oblique

c)

Rectus Abdominus

d)

Sartorius

122.

Blue

a)

Clavotrapezius

b)

Latissimus Dorsi

c)

External Oblique

d)

Brachioradialis

123.

Blue

a)

Lateral Head of Triceps Brachii

b)

Levator Scapula

c)

Long Head of Triceps Brachii

d)

Brachioradialis

124.

Pink

a)

Gastrocnemius

b)

Biceps Femoris

c)

Sartoris

d)

Spinodeltiod

Precalculus Fall 2023 Final

Total questions: 124

Worksheet time: 2hrs 4mins

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