Square Root and Absolute Value Graphs

Square Root and Absolute Value Graphs

by Kimberlee Joy

​Absolute Value Graphs

Multiple Choice

What is the equation of the absolute value function?

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

Multiple Choice

Which function defines the graph?

• f(x) = |x - 4| + 3

• f(x) = |x - 3| + 4

• f(x) = |-x + 4| + 3

• f(x) = |x + 4| + 3

Multiple Choice

What is the equation of the graph below?

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

Multiple Choice

What is the equation of this graph?

• y=2|x-3|+1

• y=2|x-1|+3

• y=-2|x+1|+3

• y=-2|x-1|+3

​Square Root Graphs

Multiple Choice

Which is the equation of the graph shown?

Scroll to see entire equation

• $$y=-\sqrt[]{x+1}+4$$

• $$y=-\sqrt[]{x-1}+4$$

• 
  $$y=\sqrt[]{x-1}+4$$

• 
  $$y=\sqrt[]{x+1}+4$$

Multiple Choice

Which is the equation of the graph shown?

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• $$y=-\sqrt[]{x}-3$$

• $$y=-\sqrt[]{x-3}$$

• $$y=\sqrt[]{x}-3$$

• 
  $$y=\sqrt[]{x-3}$$

Multiple Choice

Which is the equation of the graph shown?

Scroll to see entire equation

• $$y=\sqrt[]{x+1}-5$$

• 
  $$y=\sqrt[]{x-1}-5$$

• 
  $$y=\sqrt[]{x-5}-1$$

• 
  $$y=\sqrt[]{x+5}-1$$

Multiple Choice

Which is the equation of the graph shown?

Scroll to see entire equation

• $$y=\sqrt[]{x+2}+3$$

• $$y=\sqrt[]{x-2}+3$$

• $$y=\sqrt[]{x-3}+2$$

• 
  $$y=\sqrt[]{x+3}+2$$

​Domain (x)

​Range (y)

Multiple Choice

What is the DOMAIN of the function?

• x is all real #s

• x > 3

• x > -4

• y > 3

Multiple Choice

What is the RANGE of the function?

• y is all real #s

• y > 3

• y > 4

• 3 ≤ y ≤ 7

Multiple Choice

What is the DOMAIN of the function?

• x is all real #

• x > 1

• x < 1

• y ≤ 2

Multiple Choice

What is the RANGE of the function?

• y is all real #s

• y > 2

• y < 2

• y ≤ 1

​Domain (x)

​Range (y)

Multiple Choice

What is the DOMAIN of the function in this graph?

• x ≤ 3
• x ≥ 3
• x ≤ 0
• x ≥ 0

Multiple Choice

What is the RANGE of the function in this graph?

• y ≤ 3
• y ≥ 3
• y ≤ 0
• y ≥ 0

Multiple Choice

What is the DOMAIN of this graph?

• x ≥ -1
• x ≤ -1
• x ≥ 0
• x ≤ 0

Multiple Choice

What is the RANGE of this graph?

• y ≥ -1

• y ≤ -1

• y ≥ 0

• y ≤ 0

​Transformations

• ​A: reflect (negative)​

​ stretch (above 1)

​ compress (between 0 and 1)

​

• ​B: right (minus)

​ left (plus)

​

• ​C: up (plus)

​ down (minus)

​

​Reflected (A is negative)

​Left 2 (C plus)

​Up 3 (D plus)

Multiple Choice

Describe the transformation from the Absolute Value Parent Function.

• Stretches more narrow, shifts right
• Stretches wider, shifts right
• Stretches more narrow, shifts left
• Stretches wider, shifts left

Multiple Choice

Describe the transformations of the absolute value equation.

• Reflects over x-axis, compresses wider, shifts right 1 unit
• Reflects over x-axis, compresses wider, shifts up 1 unit
• Reflects over x-axis, stretches more narrow, shifts right 1 unit
• Reflects over x-axis, stretches more narrow, shifts up 1 unit

Multiple Choice

Describe the transformation.

• Down 1
• Reflect over y-axis
• Up 1
• Reflect over x-axis

Multiple Choice

What are the transformations of this functions compared to the parent function?

• Shifted down 2
• Shifted up 2
• Shifted left 2
• Shifted right 2

Multiple Choice

What are the transformations of this functions compared to the parent function?

• Shifted right 5, shifted down 2, and reflected over the x-axis
• Reflected over the x-axis, vertical stretch, and shifted right 5
• Reflected over the x-axis, vertical stretch, and shifted left 5
• Shifted right 5, shifted down 2

Multiple Choice

What are the transformations to the graph compared to the parent function?

• Shifted right 2, shifted up 3, and reflected over the y-axis
• Shifted left 2, shifted up 3, and reflected over the y-axis
• Shifted left 2, shifted up 3, and reflected over the x-axis
• Shifted right 2, shifted up 3, and reflected over the x-axis