Free Printable RLM Graphs of Functions Quiz

1.

Find the equation of the transformed graph

a)

$y=x^2+3$

b)

$y=\left(x+3\right)^2$

c)

$y=\ x^2-3$

d)

$y=\left(x-3\right)^2$

2.

Find the equation of the transformed graph

a)

$y=x^2+3$

b)

$y=\left(x+3\right)^2$

c)

$y=\ x^2-3$

d)

$y=\left(x-3\right)^2$

3.

a)

$y=\ \left|x\right|\ -\ 1$

b)

$y=\ -\ \left|x\right|\$

c)

$y=\ \left|x\right|\$

d)

$y=\ \left|x-1\right|$

4.

a)

$y=\ \left|x\right|\ +\ 3$

b)

$y=\ \left|x\right|-\ 3$

c)

$y=\ \left|x+3\right|\$

d)

$y=\ \left|x-3\right|$

5.

a)

$y=\ \left|x\right|\ +\ 3$

b)

$y=\ \left|x\right|-\ 3$

c)

$y=\ \left|x+3\right|\$

d)

$y=\ \left|x-3\right|$

6.

$y=3\left|x\right|$

Which graph represents this transformed function

a)

b)

c)

d)

7.

$y=-2\left|x\right|$

Which graph represents this transformed function

a)

b)

c)

d)

8.

Which equation describes the transformation of shifting f(x)=x² two units right?

a)

x² + 2

b)

x² - 2

c)

(x + 2)²

d)

(x - 2)²

9.

Describe the transformations that maps
y = g(x) to y = - g(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

10.

Given f(x) = (x-3)² + 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

11.

.
If the blue is f(x)=x^2,then the red must be

a)

g(x)=x²-5

b)

g(x)=x²+5

c)

g(x)=(x-5)²

d)

g(x)=(x+5)²

12.

What do we call the highest or lowest point of a quadratic?

a)

parabola

b)

vertex

c)

graph

d)

point

13.

Identify the y-intercept

a)

(0, -3)

b)

(0, 1)

c)

(0, 3)

d)

(2, 1)

14.

What is the domain of the graph?

a)

All real numbers

b)

To infinity and beyond

c)

y ≥ 0

d)

x ≥ 0

15.

What is the range of the graph?

a)

All real numbers

b)

To infinity and beyond

c)

y ≥ 0

d)

x ≥ 0

16.

What is the domain of the graph?

a)

All real numbers

b)

To infinity and beyond

c)

y ≥ -1

d)

x ≥ 0

17.

What is the domain of the graph?

a)

All real numbers

b)

To infinity and beyond

c)

y ≥ -1

d)

x ≥ 0

18.

What is the range of the graph?

a)

All real numbers

b)

To infinity and beyond

c)

y ≥ -1

d)

x ≥ 0

19.

What variable represents the domain?

a)

x

b)

y

c)

d

d)

r

20.

What variable represents the domain?

a)

x

b)

y

c)

d

d)

r

21.

What variable represents the range?

a)

x

b)

y

c)

d

d)

r

22.

What is the Domain of this exponential function?

a)

y=1

b)

x=0

c)

All Real Numbers

d)

x>0

23.

What is the Range of this function?

a)

y > 0

b)

x> 0

c)

All Real Numbers

d)

y > 1

24.

What is the Range of this function?

a)

y > 0

b)

x> 0

c)

All Real Numbers

d)

y > 1

25.

What is the range of the exponential function?

a)

all real numbers

b)

y > -1

c)

y < -1

d)

x > -1

26.

What is the range of the exponential function?

a)

all real numbers

b)

y > 3

c)

y < 3

d)

x > 3

27.

What is the domain of the exponential function?

a)

all real numbers

b)

y > 3

c)

y < 3

d)

x > 3

28.

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)

29.

The vertex of the quadratic function f(x) in the picture is (-4, 5). If g(x) = f(x + 2) , what is the vertex of g(x)?

a)

(-2, 5)

b)

(-6, 5)

c)

(-4, 3)

d)

(-4, 7)

30.

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

-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

31.

Describe the transformation:

g\left(x\right)=\left(x-3\right)^2

a)

Shift 3 units up

b)

Shift 3 units down

c)

Shift 3 units left

d)

Shift 3 units right

32.

Describe the transformation:

h\left(x\right)=x^2+7

a)

Shift 7 units down

b)

Shift 7 units up

c)

Shift 7 units left

d)

Shift 7 units right

33.

Describe the transformation: (click on two answers)

h\left(x\right)=\left(x-1\right)^2+5

a)

Shift 1 unit left

b)

Shift 1 unit right

c)

Shift 5 units up

d)

Shift 5 units down

34.

Describe the transformation: (click on two answers)

f\left(x\right)=-x^2-7

a)

Reflection over the x-axis

b)

Reflection over the y-axis

c)

Shift 7 units up

d)

Shift 7 units down

35.

If the blue graph is the parent function, what is the equation of the red (transformed) function?

a)

g(x)=x³+1

b)

g(x)=x³-1

c)

g(x)=(x-1)³

d)

g(x)=(x+1)³

36.

The graph shows the function f(x)=x² in blue and another function g(x) in red. Which could be the equation for g(x)?

a)

A. g(x)=3x²

b)

B. g(x)=-3x²

c)

C. g(x) = x² - 3

d)

D. g(x) = (x-3)²

37.

If the blue function is f(x)=√x, the red function must be

a)

g(x)=√(-x)

b)

g(x)=√(x-1)

c)

g(x)=√x-1

d)

g(x)=-√x

38.

DOMAIN?

a)

(-∞,∞)

b)

[0,∞)

c)

(-∞,0]

d)

-2, 2

39.

Which equation describes the transformation of shifting f(x)=x³ four units down?

a)

x³+ 4

b)

x³- 4

c)

(x - 4)³

d)

(x + 4)³

40.

Which equation describes the transformation of shifting f(x)=x³ three units left?

a)

x³ + 3

b)

x³ - 3

c)

(x + 3)³

d)

(x - 3)³

41.

a)

f(x) = −(x−2)³−1

b)

f(x) = −(x+2)³−1

c)

f(x) = −(x−2)³ + 1

d)

f(x) = −(x+2)³ + 1

42.

What is the equation of this graph?

a)

f(x) = (x + 2)² - 3

b)

f(x) = (x - 2)² - 3

c)

f(x) = |x + 2| - 3

d)

f(x) = |x - 2| - 3

43.

Identify the transformation from the graph of f(x)=x²to the graph g(x)= -(x+5)²

a)

shifted up five units

reflection in x-axis

b)

shifted down five units

reflection in x-axis

c)

shifted left 5 units

reflection x-axis

d)

shifted right 5 units

reflection x-axis

44.

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

a)

Reflect over y-axis
Left 3

b)

Reflect over y-axis
Right 3

c)

Reflect over x-axis
Left 3

d)

Reflect over x-axis
Right 3

45.

a)

$y=\ \left|x\right|\ +\ 3$

b)

$y=\ \left|x\right|-\ 3$

c)

$y=\ \left|x+3\right|\$

d)

$y=\ \left|x-3\right|$

46.

Which of the following represents the graph below?

a)

b)

c)

d)

47.

Which of the following represent the graph?

a)

b)

c)

d)

48.

What is the vertical asymptote of the following function?

a)

x = -2

b)

x = 2

c)

y = -3

d)

y = 3

49.

Describe the transformation of the function.

a)

shift left 3 units

b)

shift right 3 units

c)

shift up 3 units

d)

shift down 3 units

50.

Describe the transformations of the function.

a)

Shifted right by 4 units

Shifted down by 7 units

Stretched Vertically

b)

Shifted right by 4 units

Shifted up by 7 units

Stretched Vertically

c)

Shifted right by 4 units

Shifted down by 7 units

Compressed Vertically

d)

Shifted left by 4 units

Shifted down by 7 units

Compressed Vertically

51.

What is this function called?

a)

Quadratic

b)

Reciprocal

c)

Polynomial

d)

Exponential

52.

What is the equation of the Vertical Asymptote of $y=\frac{3}{x-4}+2$

a)

$x=2$

b)

$y=2$

c)

$x=4$

d)

$y=4$

e)

No Vertical Asymptote

53.

Which is the graph of the rational equation:

a)

b)

c)

d)

54.

What are the asymptotes?

a)

x= -1& y = -3

b)

x= 1& y = -3

c)

x= -1& y =3

d)

x= 1& y=3

55.

The given graphed function would have a horizontal asymptote at

a)

x = 0

b)

y = 0

c)

x = 2

d)

y = 2

56.

What is the domain for the following function?

a)

All real numbers except 2.

b)

All real number except -2.

c)

All real numbers except 4.

d)

All real numbers.

57.

What is the range for the following function?

a)

All real numbers.

b)

All real numbers except for -2.

c)

All real numbers except for 2.

d)

All real numbers exceptt for 4.

58.

What is the vertical asymptote of the following function?

a)

x = -2

b)

x = 2

c)

y = -3

d)

y = 3

59.

Describe the transformations of the function.

a)

Shifted right by 4 units

Shifted down by 7 units

Stretched Vertically

b)

Shifted right by 4 units

Shifted up by 7 units

Stretched Vertically

c)

Shifted right by 4 units

Shifted down by 7 units

Compressed Vertically

d)

Shifted left by 4 units

Shifted down by 7 units

Compressed Vertically

60.

Describe the transformation of the function.

a)

Shift left by 2 units

Compressed vertically

b)

Shift right by 2 units

Stretched vertically

c)

Shift right by 2 units

Compressed vertically

d)

Shift down by 2 units

Compressed vertically

61.

What is the vertical asymptote of the function?

a)

x = 2

b)

x = -2

c)

x = 0

d)

x = 1

62.

What is the horizontal asymptote of the function?

a)

x =1

b)

x = -2

c)

x = 2

d)

y = 0

63.

Given the function y = 3/x what is the domain

a)

R except x = 0

b)

R except x = 3

c)

R except y = 0

d)

R except x = 1

64.

What is the equation of the graphed function?

a)

y = (1 / x) + 2

b)

y = (1 / x) - 2

c)

y = 1 / (x + 2)

d)

y = 1 / (x - 2)

65.

What is the equation of the absolute value function?

a)

f(x)= |x+4|

b)

f(x)= |x-4|

c)

f(x)= |x| + 4

d)

f(x)= |x| - 4

66.

What is the equation of the graph below?

a)

f(x) = I x + 2 I

b)

f(x) = I x + 2 I +2

c)

f(x) = I x - 2 I +2

d)

f(x) = I x - 2 I

67.

What is the vertex of the absolute value function?

a)

(4, 0)

b)

(0, 4)

c)

(-infinity, infinity)

d)

[4, infinity)

68.

Determine the transformation

a)

left 3, up 2

b)

right 3, up 2

c)

left 3, down 2

d)

right 3, down 2

69.

.
The blue graphs is the parent function f(x)=|x|, the red must be

a)

g(x)=|x+2|

b)

g(x)=|x|+2

c)

g(x)=|x-2|

d)

g(x)=|x|-2

70.

y = |x| - 7 makes the graph slide . . .

a)

left 7

b)

right 7

c)

up 7

d)

down 7

71.

y = |x - 3| makes the graph slide . . .

a)

left 3

b)

right 3

c)

up 3

d)

down 3

72.

What is the equation of this graph?

a)

y=2|x-3|+1

b)

y=2|x-1|+3

c)

y=-2|x+1|+3

d)

y=-2|x-1|+3

73.

Use Narrow, wide, or same to compare the width of this graph to the parent function.
y=4|x+3|-2

a)

Narrow

b)

Wide

c)

Same

74.

Use Narrow, wide, or same to compare the width of this graph to the parent function.

y= 1/2 |x-1|+2

a)

Narrow

b)

Wide

c)

Same

75.

What is the axis of symmetry for the following graph?

a)

y=3

b)

x=3

c)

x=2

d)

y=2

e)

y=0

76.

What is the axis of symmetry for the following graph?

a)

y=-4

b)

x=-4

c)

x=-3

d)

y=-3

e)

x=3

77.

What is the vertex of the graph below? You can click the picture to zoom in!

a)

(-2, 0)

b)

(2, 4)

c)

(4, 2)

d)

(0, 2)

78.

Where would the asymptote be for this graph?

a)

y = 4

b)

y = -4

c)

x = 3

d)

x = -3

79.

What is the transformation?

a)

Left 5

b)

Right 5

c)

Up 5

d)

Down 5

80.

What is the asymptote of y = 2^x - 3

a)

y = 0

b)

y = -3

c)

x = 0

d)

x = -3

81.

Which equation matches the graph?

a)

y = 2^x+3

b)

y = 2^x + 3

c)

y = 2^x

d)

y = 2^-x

82.

What equation matches the graph?

a)

f(x) = 3^x

b)

f(x) = (⅓)^x

c)

f(x) = -3^x

83.

What is the y-intercept of the function?

a)

2

b)

3

c)

1

d)

-2

84.

Write the equation of the graph.

a)

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

b)

f(x) = 3^x - 2

c)

f(x) = 3^x + 2

d)

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

85.

What is the asymptote of y = 2^x-3 ?

a)

y = 0

b)

y = -3

c)

x = 0

d)

x = -3

86.

Which equation matches the graph?

a)

y = 4^x + 3

b)

y = 4^x - 3

c)

y = 4^{x + 3}

d)

y = 4^{x - 3}

87.

Which equation matches the graph?

a)

y = 4^{x + 3}

b)

y = 4^{x - 3}

c)

y = 4^x + 3

d)

y = 4^x - 3

88.

Which equation matches the graph?

a)

y = 4^{x - 6} - 3

b)

y = 4^{x + 6} - 3

c)

y = 4^{x - 6} + 3

d)

y = 4^{x + 6} + 3

89.

What is the vertex of this quadratic equation?

y = - (x + 2)² + 4

a)

(-2, 4)

b)

(2, 4)

c)

(4,-2)

d)

(-4,-2)

90.

What is the vertex of this quadratic equation?

y = 2(x - 2)² + 4

a)

(-2, 4)

b)

(2, 4)

c)

(4, 4)

d)

(2, -4)

91.

The graph of a quadratic will always be ...

a)

a line

b)

a V

c)

a parabola

d)

a squiggle

92.

What is the vertex of the parabola: y=2(x-3)²+4

a)

(3,4)

b)

(-3,4)

c)

(3, -4)

d)

(-3,-4)

93.

What is the vertex of the parabola:

y=2(x + 3)²+4

a)

(3,4)

b)

(-3,4)

c)

(-6, 4)

d)

(-6,-4)

94.

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

95.

Identify the vertex and whether the graph opens up or down.

a)

(5, 2); opens up

b)

(5, 2); opens down

c)

(-5, 2); opens up

d)

(-5, 2); opens down

96.

What is the vertex of this parabola?

y = x² + 5

a)

(5, 0)

b)

(-5, 0)

c)

(0, 5)

d)

(0, 0)

97.

What is the vertex of this parabola?

y = (x+7)²

a)

(49, 0)

b)

(-7, 0)

c)

(0, 7)

d)

(0, -7)

98.

What is the equation of this graph?

a)

f(x) = (x -5)² + 1

b)

f(x) = (x - 1)² - 5

c)

f(x) = (x + 1)² - 5

d)

f(x) = (x + 5)² +1

99.

A parabola has a vertex at (-3,2).
Where is the axis of symmetry?

a)

y = -2

b)

x = 3

c)

x = -3

d)

y = 2

100.

What is the axis of symmetry of the given function?

a)

y = 1

b)

y = -1

c)

x = 1

d)

x = -1

101.

Find the vertex:

y = -5(x + 1)² - 8

a)

(-1, -8)

b)

(1, -8)

c)

(-1. 8)

d)

(1, 8)

102.

Find the axis of symmetry:

y = ½(x + 3)² + 4

a)

x = -3

b)

x = 3

c)

x = 4

d)

x = -4

103.

Find the y-intercept of:

y=2(x - 3)²+ 4

a)

22

b)

10

c)

-14

d)

13

104.

Find the y-intercept:

y = -5(x + 1)² - 8

a)

-13

b)

13

c)

3

d)

12

105.

What is the vertex, axis of symmetry, does the graph opens up or down, domain and range of the given parabola:

y=6(x-4)²-1?

a)

Vertex: (4,-1)

Axis of Symmetry: x=4

Graph opens: up

Domain: all real numbers

Range: y≥-1

b)

Vertex: (4,-1)

Axis of Symmetry: x = 4

Graph opens: up

Domain: x≥-1

Range: all real numbers

c)

Vertex: (-4,1)

Axis of symmetry: y=-1

Graph opens: up

Domain: all real numbers

Range: y ≤-1

d)

Vertex: (-4,1)

Axis of symmetry: x=-4

Graph opens: up

Domain: x≤-1

Range: all real numbers

106.

Which of the following is the correct equation for the given graph?

a)

f(x) = (x - 2)² - 1

b)

f(x) = (x + 2)² - 1

c)

f(x) = -(x + 2)² - 1

d)

f(x) = -(x - 2)² - 1

107.

Describe the transformation below: $-\left(x+3\right)^2+6$

a)

reflect over the x-axis

b)

reflect over the x-axis, left: 3, up: 6

c)

stretch, left: 3, down: 6

d)

left: 3, down: 6

108.

Describe the transformation below: $-3\left(x+4\right)^2-1$

a)

stretch by 3, right: 4, down: 1

b)

reflect over the x-axis, right: 4, down: 1

c)

reflect over the x-axis, stretch by 3, left: 4, down: 1

d)

stretch by 4, down: 3, left: 1

109.

Determine if the following function will be narrow (stretch) or wider (shrink): $4\left(x-3\right)^2+4$ (a)

Choose from the below words

Narrow

Wider

110.

Determine if the following is narrow or wider: $\frac{2}{3}\left(x+3\right)^2+6$ (a)

Choose from the below words

Narrow

Wider

111.

What is a quadratic funtion in the form of $f\left(x\right)=a\left(x-h\right)^2+k$ called? (a)

Choose from the below words

Factored Form

Standard Form

Vertex Form

112.

What is the vertex of $f\left(x\right)=\left(x+4\right)^2$

a)

(0,4)

b)

(4,0)

c)

(-4,0)

d)

(0,-4)

113.

$f\left(x\right)=-\left(x-4\right)^2+1$ Choose the correct graph of the equation.

a)

b)

c)

d)

114.

Transformation:
Which describes the transformation of the graph f(x) = x² to the graph of g(x) = 5x² ?

a)

The graph of g(x) is wider.

b)

The graph of g(x) is narrower

c)

The graph of g(x) reflects

d)

The graph of g(x) is to the right

115.

Which quadratic function is represented by 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

116.

Which of the following equations matches vertex form of a quadratic?

a)

ax + by = c

b)

y = a(x - h)² + k

c)

y = ax² + bx + c

d)

y = mx + b

117.

Which equation is graphed above?

a)

$y=-\left(x-1\right)^2+4$

b)

$y=\left(x-1\right)^2+4$

c)

$y=-\left(x-4\right)^2+1$

d)

$y=\left(x-4\right)^2+1$

118.

Explain the transformation of

y=(x+3)² - 1

a)

right 3 , down 1

b)

Left 3, down 1

c)

left 1, Down 3

d)

Right 1, UP 3

119.

What is this quadratic equation called ?

y = x²

a)

Mom and Pop

b)

Home base

c)

the Goal

d)

the Parent function

120.

What is the only transformation of this equation

y= - x²

a)

up 1

b)

down 1

c)

reflected ( flipped)

d)

wider ( shrink)

121.

Which quadratic function is represented by 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

122.

Does this graph show a maximum or a minimum?

a)

Maximum

b)

Minimum

123.

Where is the axis of symmetry for this parabola?

a)

x = −1

b)

x = 0

c)

y = 3

d)

x = −3

124.

Use the graph to determine the x-intercepts.

a)

-1 and -3

b)

1 and -3

c)

1 and 3

d)

-1 and 3

125.

Which of the following describes the transformations done to the quadratic parent function of f(x) = x² to obtain g(x) = 2x² + 4 ?

a)

Vertical Stretch by a factor of 2 and vertical shift up 4 units

b)

Vertical Compress by a factor 2 and vertical shift up 4

c)

Vertical Stretch by a factor of 2 and horizontal shift left 4 units

d)

Vertical Compress by a factor of 2 and horizontal shift right 4 units

126.

What is the equation of the quadratic function obtained from vertically compressing the parent function by 3/5 and then shifted up 8 units?

a)

f(x)= 3/5(x-8)²

b)

f(x)=3/5x²+8

c)

f(x)=x²

d)

f(x)=3/5x²-8

127.

What is the equation of the quadratic function obtained from vertically compressing the parent function by a factor of 0.5 and then reflecting across the x-axis?

a)

f(x)= 0.5x²

b)

f(x)= -0.5x²

c)

f(x)= -(x-0.5)²

d)

f(x)= x²+0.5

128.

If the blue graph is
f(x) = x²
then the red must be...

a)

g(x) = x²- 5

b)

g(x) = x²+ 5

c)

g(x) = (x - 5)²

d)

g(x) = (x + 5)²

RLM Graphs of Functions Quiz

Total questions: 128

Worksheet time: 6hrs 27mins

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