Absolute Value Transformations: Vertical Insights

The video tutorial explains the concept of transforming the parent function of absolute value, focusing on vertical translation. It highlights the difference between horizontal and vertical transformations, emphasizing that changes outside the absolute value affect vertical shifts. The tutorial demonstrates how to graph the transformed function, identify the vertex, and determine the axis of symmetry. It concludes by analyzing graph data to confirm predictions about the function's behavior.

What is the parent function of the absolute value?

• y = x^3

• y = |x|

• y = 1/x

• y = x^2

What happens when a value is added or subtracted inside the absolute value?

• Vertical translation

• Horizontal translation

• Dilation

• Reflection

Where is the value placed for a vertical translation?

• Inside the absolute value

• Outside the absolute value

• In the denominator

• In the exponent

What is the vertex of the function y = |x| - 4?

• (-4, 0)

• (4, 0)

• (0, 4)

• (0, -4)

How do you determine the axis of symmetry for the function y = |x| - 4?

• It is always x = 1

• It is the y-value of the vertex

• It is the x-value of the vertex

• It is always y = 0

What is the axis of symmetry for the function y = |x| - 4?

• x = 4

• x = -4

• x = 0

• x = 1

What happens to the graph of y = |x| when it is transformed to y = |x| - 4?

• It shifts left by 4 units

• It shifts down by 4 units

• It shifts right by 4 units

• It shifts up by 4 units

What is the y-value of the vertex for the function y = |x| - 4?

• 1

• 4

• -4

• 0

What is the equation of the y-axis?

• y = 1

• x = 1

• y = 0

• x = 0

What does a negative value outside the absolute value function indicate?

• The graph shifts up

• The graph shifts down

• The graph shifts left

• The graph shifts right