Free Printable A2-CHAPTER 1 TEST 2025-26

1.

Which parent function matches the graph?

a)

y = |x|

b)

y = x

c)

y = x²

d)

y = 2^x

2.

What type of function is shown?

a)

absolute value

b)

quadratic

c)

linear

d)

exponential

3.

What type of function is shown?

a)

linear

b)

quadratic

c)

square root

d)

absolute value

4.

Name the parent function.

a)

linear

b)

quadratic

c)

cube root

d)

cubic

5.

Name the parent function.

a)

constant

b)

square root

c)

linear

d)

absolute value

6.

Which equation below is a quadratic function translated up 5 units?

a)

y = x² + 5

b)

y = (x + 5)²

c)

y = 5x²

d)

y = -x² - 5

7.

What type of function is shown?

a)

cube root

b)

square root

c)

logarithm

d)

exponential

8.

Which equation below is a quadratic function translated left 4 units?

a)

y = x² + 4

b)

y = (x + 4)²

c)

y = (x - 4)²

d)

y = 4x²

9.

Which equation is a quadratic function reflected over the x-axis and shifted up 2.

a)

y = x² + 2

b)

y = -x² + 2

c)

y = x² - 2

d)

y = -(x + 2)²

10.

Describe the transformation

a)

left 2 up 5

b)

right 2 up 5

c)

left 2 down 5

d)

right 2 down 5

11.

Which equation is an absolute value graph shifted right 5 units?

a)

y = |x - 5|

b)

y = |x + 5|

c)

y = |x| + 5

d)

y = -5|x|

12.

Tell how the graph transformed.
y = (x - 3)²

a)

Translated right 3

b)

Translated left 3

c)

Translated up 3

d)

Translated down 9

13.

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

a)

g(x)=(x+3)²

b)

g(x)=(x-3)²

c)

g(x)=x²+3

d)

g(x)=x²-2

14.

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

15.

Which transformation maps the graph of
f(x) = x² to the graph of g(x) = (x + 4)²?

a)

a translation shifting f(x) 4 units up

b)

a translation shifting f(x) 4 units down

c)

a translation shifting f(x) 4 units to the left

d)

a translation shifting f(x) 4 units to the right

16.

a)

Left 2, Down 2, Vertical Stretch

b)

Right 2; Up 1;

c)

Vertical Stretch; Right 2; Up 1

d)

Left 2; Down 2;

17.

Describe the transformation of the equation below from the parent function of y = I x I
y = -2 I x - 3 I + 3

a)

reflected over x axis, stretched by 2, right 3, up 3

b)

reflected over x axis, stretched by 2, left 3 up 3.

c)

reflected over x axis, shrunk by 2, right 3, up 3

d)

reflected over the x axis, shrunk by 2, left 3, up 3

18.

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

19.

Describe the transformation of the equation below from the parent function of y = I x I
y = I x - 4 I

a)

Left 4

b)

Right 4

c)

Up 4

d)

Down 4

20.

If the blue function is f(x)=x², then the red function must be

a)

g(x)=x²-5

b)

g(x)=x²+5

c)

g(x)=(x-5)²

d)

g(x)=(x+5)²

21.

Describe the transformation of y = f(x) for the new function
y = f(x) - 5

a)

The graph of y = f(x) was shifted to the right 5 units.

b)

The graph of y = f(x) was shifted to the left 5 units.

c)

The graph of y = f(x) was shifted up 5 units.

d)

The graph of y = f(x) was shifted down 5 units.

22.

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

23.

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

24.

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

25.

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

26.

Describe the transformation from the parent graph

a)

Reflect over x, right 3, down 4

b)

Reflect over y, right 3, down 4

c)

Reflect over x, right 3, up 4

d)

Reflect over y, left 3, down 4

27.

Which equation is a quadratic function reflected over the x-axis and shifted up 2.

a)

y = x² + 2

b)

y = -x² + 2

c)

y = x² - 2

d)

y = -(x + 2)²

28.

Which equation below is a quadratic function translated left 4 units?

a)

y = x² + 4

b)

y = (x + 4)²

c)

y = (x - 4)²

d)

y = 4x²

29.

Describe the transformations of f(x) when compared to the parent function.
f(x)=x²+5

a)

horizontal shift right 5 units

b)

horizontal shift left 5 units

c)

vertical shift up 5 units

d)

vertical shift down 5 units

30.

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

31.

Which is an example of a function shifting downward 2 units and to the right 3 units

a)

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

b)

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

c)

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

d)

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

32.

Which of the following describes the horizontal and vertical translations of the following functions:
f(x) = |x + 4| - 9

a)

Left 4
up 9

b)

Left 4
Down 9

c)

Right 4
up 9

d)

Right 4
Down 9

33.

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

34.

Describe the transformation of y = f(x) to the new function
y = f(1/5x)

a)

Horizontal shrink by a factor of 1/5

b)

Vertical stretch be a factor of 5

c)

Vertically shrink by a factor of 1/5

d)

Horizontal stretch by a factor of 5

35.

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

36.

Describe the transformation from the Absolute Value Parent Function.

a)

Stretches more narrow, shifts up 4 units

b)

Stretches more narrow, shifts down 4 units

c)

Compresses wider, shifts up 4 units

d)

Compresses wider, shifts down 4 units

37.

Which of the following describes the horizontal and vertical translations of the following functions:
f(x) = |x + 4| - 9

a)

Left 4
up 9

b)

Left 4
Down 9

c)

Right 4
up 9

d)

Right 4
Down 9

38.

Write an absolute value function given the following transformations:
Vertical Stretch of 2
Horizontal shift left 1 unit
Vertical shift down 9 units

a)

f(x) = |2x + 1| - 9

b)

f(x) = |2x - 1| - 9

c)

f(x) = 2|x + 1| - 9

d)

f(x) = 2|x - 1| - 9

39.

Write an absolute value function given the following transformations:
Reflection across the x-axis
Vertical shift right 2 units
Horizontal shift down 7 units

a)

y = -|x + 2| - 7

b)

y = |x - 2| - 7

c)

y = -|x - 2| - 7

d)

y = -|x - 2| + 7

40.

How did we transform from the parent function?

g(x) = -5(x - 1)² + 7

a)

reflection, vertical stretch, right 1, vertical up 7

b)

reflection, vertical compression, right 1, up 7

c)

reflection, vertical stretch, left 1, up 7

d)

no changes were made to y = x²

41.

What transformations have occurred?

a)

Right 2 and up 2

b)

Left 2 and up 2

c)

Right 2 and down 2

d)

Left 2 and down 2

42.

What change does a Translation Cause?

a)

a shift up, down, left, or right

b)

a reflection

c)

a compression

d)

a stretch

43.

Which equation below is a quadratic function translated up 5 units?

a)

y = x² + 5

b)

y = (x + 5)²

c)

y = 5x²

d)

y = -x² - 5

44.

Which equation below is a quadratic function translated left 4 units?

a)

y = x² + 4

b)

y = (x + 4)²

c)

y = (x - 4)²

d)

y = 4x²

45.

What does the transformation $f\left(x\right)\ \rightarrow\ f\left(x+1\right)-9$ do to the graph of $f\left(x\right)$ ?

a)

translates it left one unit and down 9 units

b)

translates it right one unit and down 9 units

c)

translates it up one unit and right 9 units

d)

translates it down one unit and left 9 units

46.

g(x)=f(x-4)
Describe the transformation to f(x) that results in g(x).

a)

f(x) has been translated to the right 4.

b)

f(x) has been translated to the left 4.

47.

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

48.

Name the parent function.

a)

quadratic

b)

cubic

c)

square root

d)

logarithmic

49.

Name the parent function.

a)

linear

b)

constant

c)

absolute value

d)

quadratic

50.

.
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

51.

Describe the transformation: g(x) = f(x)+2

a)

The graph moved down 2

b)

The graph moved up 2

c)

The graph moved to the right 2

d)

The graph moved to the left 2

52.

Describe the transformation: g(x) = f(x)-4

a)

The graph moved up 4

b)

The graph moved down 4

c)

The graph moved to the right 4

d)

The graph moved to the left 4

53.

Describe the transformation: g(x) = f(x-3)

a)

The graph moved up 3

b)

The graph moved down 3

c)

The graph moved to the right 3

d)

The graph moved to the left 3

54.

Describe the transformation: g(x) = f(x-1)+7

a)

The graph moved up 7 and to the right 1

b)

The graph moved up 7 and to the left 1

c)

The graph moved down 7 and to the right 1

d)

The graph moved down 7 and to the left 1

55.

Describe the transformation: g(x) = f(x+2)+3

a)

The graph moved up 3 and to the right 2

b)

The graph moved up 3 and to the left 2

c)

The graph moved down 3 and to the right 2

d)

The graph moved down 3 and to the left 2

56.

What equation represents the quadratic function?

a)

y = (x - 4)²

b)

y = (x + 4)²

c)

y = x² - 4

d)

y = x² + 4

57.

What equation represents the quadratic function?

a)

y = (x - 8)²

b)

y = (x + 8)²

c)

y = x² - 8

d)

y = x² + 8

58.

What equation represents the quadratic function?

a)

y = (x - 7)² - 2

b)

y = (x + 7)² + 2

c)

y = (x + 7)² - 2

d)

y = (x + 2)² + 7

59.

What equation represents the quadratic function?

a)

y = (x - 5)² - 3

b)

y = (x - 5)² + 3

c)

y = (x + 5)² - 3

d)

y = (x - 3)² - 5

60.

What equation represents the quadratic function?

a)

y = (x - 4)² + 1

b)

y = (x + 1)² - 4

c)

y = (x - 4)² - 1

d)

y = (x - 1)² - 4

61.

What does the transformation $f\left(x\right)\ \rightarrow\ f\left(x+1\right)-9$ do to the graph of $f\left(x\right)$ ?

a)

translates it left one unit and down 9 units

b)

translates it right one unit and down 9 units

c)

translates it up one unit and right 9 units

d)

translates it down one unit and left 9 units

62.

What equation represents the quadratic function?

a)

y = (x - 4)²

b)

y = (x + 4)²

c)

y = x² - 4

d)

y = x² + 4

63.

What equation represents the quadratic function?

a)

y = (x - 8)²

b)

y = (x + 8)²

c)

y = x² - 8

d)

y = x² + 8

64.

What equation represents the quadratic function?

a)

y = (x - 5)² - 3

b)

y = (x - 5)² + 3

c)

y = (x + 5)² - 3

d)

y = (x - 3)² - 5

65.

What equation represents the quadratic function?

a)

y = (x - 4)² + 1

b)

y = (x + 1)² - 4

c)

y = (x - 4)² - 1

d)

y = (x - 1)² - 4

66.

What equation represents the quadratic function?

a)

y = (x - 8)²

b)

y = (x + 8)²

c)

y = x² - 8

d)

y = x² + 8

67.

Given the parent function

f\left(x\right)\ =x^{2\ }

, write the equation of the function with the given transformation.

Left 7 and Up 4

a)

$f\left(x\right)=\left(x-7\right)^{2\ }+\ 4$

b)

$f\left(x\right)\ =\ \left(x+7\right)^{2\ }+4$

c)

$f\left(x\right)=\left(x+7\right)^{2\ }-4$

d)

$f\left(x\right)\ =\ \left(x-7\right)^{2\ }-4$

68.

Given the parent function

f\left(x\right)\ =\ x^{2\ }

, how was the parent function transformed to create the new function?

f\left(x\right)\ =\ \frac{1}{3}\left(x-5\right)^{2\ }+7

a)

Horizontal dilation of 3, left 5, and down 7.

b)

Vertical dilation of 3, right 5, and up 7.

c)

Vertical dilation of 1/3, right 5, and up 7.

d)

Horizontal dilation of 1/3, left 5, and down 7.

69.

Given the parent function

f\left(x\right)\ =x^{2\ }

, write the equation of the function with the given transformation.

Horizontal dilation 1/7, left 2, up 5.

a)

$f\left(x\right)=\left(7x-2\right)^{2\ }+5$

b)

$f\left(x\right)\ =\ \left(\frac{1}{7}x+2\right)^{2\ }+5$

c)

$f\left(x\right)=\frac{1}{7}\left(x+2\right)^{2\ }+5$

d)

$f\left(x\right)\ =\ \left(7x+2\right)^{2\ }+5$

70.

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

71.

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

72.

What is the equation of the graph below?

a)

f(x) = - I x + 2 I

b)

f(x) = - I x - 2 I

c)

f(x) = I x + 2 I

d)

f(x) = I x - 2 I

73.

What is the equation of the graph below?

a)

f(x ) = I x + 4 I + 2

b)

f(x ) = -I x - 4 I + 2

c)

f(x ) = I x - 4 I + 2

d)

f(x ) = -I x + 4 I + 2

74.

What shifts have occurred?

a)

left 1, up 5

b)

left 1, down 5

c)

right 1, down 5

d)

right 1, up 5

75.

Which of the following describes the horizontal and vertical translations of the following functions:
f(x) = |x + 4| - 9

a)

Left 4
up 9

b)

Left 4
Down 9

c)

Right 4
up 9

d)

Right 4
Down 9

76.

Describe the transformation from the Absolute Value Parent Function.

a)

Stretches more narrow, shifts up 4 units

b)

Stretches more narrow, shifts down 4 units

c)

Compresses wider, shifts up 4 units

d)

Compresses wider, shifts down 4 units

77.

Describe the transformations of the absolute value equation.

a)

Flips to A shape, compresses wider, shifts right 1 unit

b)

Flips to A shape, compresses wider, shifts up 1 unit

c)

Flips to A shape, stretches more narrow, shifts right 1 unit

d)

Flips to A shape, stretches more narrow, shifts up 1 unit

78.

Choose the correct equation for the graph.

a)

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

b)

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

c)

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

d)

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

79.

If the blue is $f\left(x\right)=x^2$ , then the red must be

a)

$f\left(x\right)=x^2-5$

b)

$f\left(x\right)=x^2+5$

c)

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

d)

$f\left(x\right)=5x^2$

80.

Describe the transformation of y = (x - 4)²

a)

Shift UP

b)

Shift DOWN

c)

Shift LEFT

d)

Shift RIGHT

81.

Describe the transformation of y = x² + 4

a)

Shift UP

b)

Shift DOWN

c)

Shift LEFT

d)

Shift RIGHT

82.

How did we transform from the parent function?

f(x) = x² + 2

a)

shift right 2

b)

shift up 2

c)

shift down 2

d)

shift left 2

83.

The dotted line represents the parent function. The blue line represents a family member. Find the function for the transformed graph.

a)

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

b)

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

c)

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

d)

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

84.

Find the equation of the transformed graph

a)

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

b)

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

c)

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

d)

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

85.

a)

$f\left(x\right)=\ \left|x\right|\ +\ 3$

b)

$f\left(x\right)=\ \left|x\right|-\ 3$

c)

$f\left(x\right)=\ \left|x+3\right|\$

d)

$f\left(x\right)=\ \left|x-3\right|$

86.

a)

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

b)

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

c)

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

d)

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

87.

a)

$f\left(x\right)=\ \left|x\right|\ -\ 1$

b)

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

c)

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

d)

$f\left(x\right)=\ \left|x-1\right|$

88.

When you change the value of a what happens to the graph?

a)

stretches, shrinks, or flips

b)

moves up or down

c)

moves left or right

89.

When you change the value of h what happens to the graph?

a)

stretches, shrinks, or flips

b)

moves up or down

c)

moves left or right

90.

When you change the value of k what happens to the graph?

a)

stretches, shrinks, or flips

b)

moves up or down

c)

moves left or right

91.

$f\left(x\right)=x^2+10$ will do what to the graph of $f\left(x\right)=x^2$ ?

a)

move it up 10

b)

move it left 10

c)

move it right 10

d)

move it down 10

92.

How will $f\left(x\right)=\left|x+3\right|$ change $f\left(x\right)=\left|x\right|$ ?

a)

move right 3

b)

move left 3

c)

move up 3

d)

move down 3

93.

Which of these would make $f\left(x\right)=x$ shift down 5?

a)

$f\left(x\right)=x-5$

b)

$f\left(x\right)=x+5$

c)

$f\left(x\right)=5x$

d)

$f\left(x\right)=\frac{x}{5}$

94.

What is the definition of PARENT FUNCTION?

a)

the most basic function in a family

b)

x - values

c)

outputs

d)

all the functions in a family

95.

The graph of $f\left(x\right)=x^2$ is reflected over the x-axis and is stretched horizontally to create the graph of function $g.$ Which graph could represent $g?$

a)

b)

c)

d)

96.

The graph of $f\left(x\right)=x^2$ was translated 4.5 units to the left to create the graph of function $g.$ Which function represents $g?$

a)

$g\left(x\right)=\left(x-4.5\right)^2$

b)

$g\left(x\right)=\left(x+4.5\right)^2$

c)

$g\left(x\right)=x^2-4.5$

d)

$g\left(x\right)=x^2+4.5$

97.

The graph of quadratic function $f$ was transformed to create the graph of $g\left(x\right)=f\left(x+2\right)-5.$ Which graph best represents $g$ ?

a)

b)

c)

d)

98.

The graph of $f\left(x\right)=x^2\$ was transformed to create the graph of $g\left(x\right)=f\left(x\right)-9.$ Which statement about the graphs is true?

a)

The graph of $g$ is a reflection of the graph of $f$ across the x-axis.

b)

The vertex of the graph of $g$ is 9 units to the right of the vertex of the graph of $f.$

c)

The graph of $g$ is a reflection of the graph of $f$ across the y-axis.

d)

The y-intercept of the graph of $g$ is 9 units below the y-intercept of the graph of $f.$

99.

The graph of quadratic function $p$ is shown on the grid.

If $k\left(x\right)=x^2$ and $p\left(x\right)=k\left(x\right)+n,$ what is the value of $n?$

Record your answer in the blank.

100.

The graph of $g\left(x\right)=x^2$ was transformed to create the graph of $h\left(x\right)=-\left(\frac{x}{4}\right)^2$ . Which of these describes the transformation from the graph of $g$ to the graph of $h.$

a)

A reflection over the x-axis and a horizontal stretch.

b)

A reflection over the y-axis and a horizontal stretch

c)

A reflection over the x-axis and a vertical stretch

d)

A reflection over the y-axis an a vertical stretch

101.

The graph of $f\left(x\right)=x^2\$ was transformed to create the graph of $g\left(x\right)=\left(x-7.5\right)^2$ . Which of these describes this transformation?

a)

A horizontal shift to the right 7.5 units

b)

A horizontal shift to the left 7.5 units

c)

A vertical shift down 56.25 units

d)

A vertical shift up 56.25 units

102.

The graph of $f\left(x\right)=x^2$ was transformed to create the graph of $g\left(x\right)=f\left(x+6\right)^2-4$ . Which two points lie on the graph of $g\left(x\right)$ ?

Select TWO correct answers.

A

B

C

D

E

F

G

H

103.

The graph of $p\left(x\right)=x^2$ was transformed to create the graph of $r\left(x\right)=-\left(\frac{x}{3}\right)^2$

Complete the sentence to describe this transformation.

Choose the correct answer from each drop-down menu to complete the statement.

The graph of ! is reflected over the (a) and (b) stretched to create the graph of !

Choose from the below words

x-axis

horizontally

y-axis

vertically

104.

The graph of $g\left(x\right)=x^2$ was transformed to create the graph of $h\left(x\right)=3f\left(x\right)-5$ . Which of the following statements are true?

Select TWO correct answers.

a)

The graph of $h$ will be narrower than the graph of $g$

b)

The graph of $h$ will be wider than the graph of $g$

c)

The vertex of the graph of $h$ is 5 units to the right of the vetex of the graph $g$

d)

The vertex of the graph of $h$ is 5 units below the vertex of graph $g$

e)

The y-intercept of the graph of $h$ is 5 units above the vertex of graph $g$

105.

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

106.

f(x) is transformed so that it maps onto g(x). Which equation would correctly represent g(x)

a)

g(x) = x² - 3

b)

g(x) = x² + 3

c)

g(x) = (x - 3)²

d)

g(x) = (x + 3)²

107.

The vertex of the quadratic function f(x) in the picture is (-4, 5).

If g(x) = f(x) translated LEFT 2 units , what is the vertex of g(x)?

a)

(-2, 5)

b)

(-6, 5)

c)

(-4, 3)

d)

(-4, 7)

108.

The vertex of the quadratic function f(x) in the picture (2, -2).

If g(x) = f(x) translated DOWN 4 units , what is the vertex of g(x)?

a)

(2, -6)

b)

(2, 2)

c)

(-2, -2)

d)

(6, -2)

109.

Compare the function y = 0.3x² to the parent function y = x²

a)

Wider

(Vert. Compress)

b)

Narrower

(Vert. Stretch)

110.

Compare the function y = 5x² to the parent function y = x²

a)

Wider

(Vert. Compress)

b)

Narrower

(Vert. Stretch)

111.

Match the equation to its description.

a)

Reflected over x and stretched by 3

b)

Stretched by 3

c)

Reflected over x

d)

Reflected over x and down 3

112.

Match the equation to its description.

a)

Reflected over x, right 2 and up 1

b)

Reflected over x, left 2 and up 1

c)

Reflected over x, right 2 and down 1

d)

Reflected over x, left 2 and down 1

113.

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

a)

Narrow, Right, Up

b)

Narrow, Left, Down

c)

Wide, Right, Up

d)

Wide, Left, Down

114.

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

115.

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

116.

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

117.

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

118.

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

119.

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

120.

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

121.

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

122.

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

123.

a)

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

b)

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

c)

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

d)

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

124.

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

125.

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

126.

What is the equation of the graph below?

a)

f(x) = - I x + 2 I

b)

f(x) = - I x - 2 I

c)

f(x) = I x + 2 I

d)

f(x) = I x - 2 I

127.

Describe the transformation of the equation below from the parent function of y = IxI
y = I x + 2 I - 5

a)

Left 2 up 5

b)

Right 2 up 5

c)

Left 2 down 5

d)

Right 2 down 5

128.

What is the equation of the graph below?

a)

f(x ) = I x + 4 I + 2

b)

f(x ) = -I x - 4 I + 2

c)

f(x ) = I x - 4 I + 2

d)

f(x ) = -I x + 4 I + 2

129.

What shifts have occurred?

a)

left 1, up 5

b)

left 1, down 5

c)

right 1, down 5

d)

right 1, up 5

130.

What is the equation of the graph below?

a)

f(x) = I x I -1

b)

f(x) = I x I +1

c)

f(x) = - I x I -1

d)

f(x) = -I x I +1

131.

Which of the following describes the horizontal and vertical translations of the following functions:
f(x) = |x + 4| - 9

a)

Left 4
up 9

b)

Left 4
Down 9

c)

Right 4
up 9

d)

Right 4
Down 9

132.

Describe the transformation from the Absolute Value Parent Function.

a)

Stretches more narrow, shifts up 4 units

b)

Stretches more narrow, shifts down 4 units

c)

Compresses wider, shifts up 4 units

d)

Compresses wider, shifts down 4 units

133.

Describe the transformations of the absolute value equation.

a)

Flips to A shape, compresses wider, shifts right 1 unit

b)

Flips to A shape, compresses wider, shifts up 1 unit

c)

Flips to A shape, stretches more narrow, shifts right 1 unit

d)

Flips to A shape, stretches more narrow, shifts up 1 unit

134.

Write an absolute value function given the following transformations:
Vertical Stretch of 2
Horizontal shift left 1 unit
Vertical shift down 9 units

a)

f(x) = |2x + 1| - 9

b)

f(x) = |2x - 1| - 9

c)

f(x) = 2|x + 1| - 9

d)

f(x) = 2|x - 1| - 9

135.

Write an absolute value function given the following transformations:
Reflection across the x-axis
Vertical shift right 2 units
Horizontal shift down 7 units

a)

y = -|x + 2| - 7

b)

y = |x - 2| - 7

c)

y = -|x - 2| - 7

d)

y = -|x - 2| + 7

136.

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

a)

y = - | x + 2| + 4

b)

y = - | x - 2| + 4

c)

y = | x - 2 | + 4

d)

y = | x - 2| - 4

137.

Use Narrow, Wide, or Same to compare the width of this graph to its parent function.
y = 5/2 |x - 1|+ 2

a)

Narrow

b)

Wide

c)

Same

138.

Which function is graphed?

a)

f(x) = -3|x - 1| + 4

b)

f(x) = -|x - 1| + 4

c)

f(x) = -5|x + 1| + 4

d)

f(x) = -3|x - 4| + 1

139.

Determine the transformation

a)

left 3, up 2

b)

right 3, up 2

c)

left 3, down 2

d)

right 3, down 2

140.

Which function defines the graph?

a)

f(x) = |x - 4| + 3

b)

f(x) = |x - 3| + 4

c)

f(x) = |-x + 4| + 3

d)

f(x) = |x + 4| + 3

141.

What is the equation of the absolute value function?

a)

f(x)= 4|x+3|

b)

f(x)= 1/4 |x+3|

c)

f(x)= 1/4 |x - 3|

d)

f(x)= 4|x - 3|

142.

Write the equation for a graph that is vertically shrunk by a factor of 2/5 and shifted up 6.

a)

y=6|x|-2/5

b)

y=2/5|x|+6

c)

y=2/5|x+6|

d)

y=2/5|x-6|

143.

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

144.

Describe the transformation of the equation below from the parent function of y = I x I

y = -2 I x - 3 I + 3

a)

reflected over x axis, stretched by 2, right 3, up 3

b)

reflected over x axis, stretched by 2, left 3 up 3.

c)

reflected over x axis, shrunk by 2, right 3, up 3

d)

reflected over the x axis, shrunk by 2, left 3, up 3

145.

Who am I?

a)

f(x) = |x|

b)

y = x²

146.

Name the parent function family.

y=\left|x-2\right|+7

a)

Smith

b)

Constant

c)

Identity

d)

Absolute Value

e)

Quadratic

147.

Identify the transformation

(select all that apply).

f\left(x\right)=\left|x+3\right|-2

a)

Left 3

b)

Right 3

c)

Up 2

d)

Down 2

148.

Identify the transformation

(select all that apply).

f\left(x\right)=-\left|x+2\right|+3

a)

Left 2

b)

Right 2

c)

Up 3

d)

Reflect over y-axis

e)

Reflect over x-axis

149.

Describe the following transformations on the parent function ƒ(x)= |x|:

ƒ(x)= |x+1|+3

a)

Shift right 1 unit and down 3 units

b)

Shift left 1 unit and up 3 units

c)

Shift left 3 units and up 1 unit.

d)

Shift right 1 unit and up 3 units

150.

Describe the following transformation(s) on the parent function ƒ(x)= |x|:

ƒ(x)= |x|+1

a)

Shift up 1 unit

b)

Shift left 1 unit

c)

Shift right 1 unit

d)

Shift down 1 unit

151.

Describe the transformation of the equation below from the parent function of y = IxI
y = I x + 2 I - 5

a)

Left 2 up 5

b)

Right 2 up 5

c)

Left 2 down 5

d)

Right 2 down 5

A2-CHAPTER 1 TEST 2025-26

Total questions: 151

Worksheet time: 6hrs 27mins

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