Graphing Absolute Value Functions

This video tutorial covers graphing absolute value functions, focusing on transformations. It reviews the parent function and explains how to apply transformations such as vertical stretches, compressions, and reflections. The tutorial includes example problems to illustrate these concepts and discusses domain and range considerations.

What is the parent function of an absolute value function?

• y = x^3

• y = 1/x

• y = |x|

• y = x^2

What is the domain of the parent absolute value function?

• 0 to 10

• 0 to positive infinity

• Negative infinity to 0

• Negative infinity to positive infinity

What shape does the graph of an absolute value function typically have?

• U-shape

• V-shape

• S-shape

• L-shape

What does a vertical stretch by a factor of 2 do to the y-values of an absolute value function?

• Subtracts 2 from the y-values

• Halves the y-values

• Doubles the y-values

• Adds 2 to the y-values

If an absolute value function is shifted left by 5 units, how is this represented in the function?

• y = |x + 5|

• y = |x - 5|

• y = |x| + 5

• y = |x| - 5

In the example, what is the new origin after shifting the function left 5 units and down 2 units?

• (-2, -5)

• (5, 2)

• (-5, -2)

• (0, 0)

What transformation is indicated by a negative sign in front of the absolute value function?

• Vertical stretch

• Reflection over the y-axis

• Reflection over the x-axis

• Vertical compression

How do you represent a vertical compression by a factor of 1/2 in an absolute value function?

• y = 2|x|

• y = |x| + 1/2

• y = |x|/2

• y = 1/2|x|

If a function is shifted right 9 units and up 5 units, how is this represented in the function?

• y = |x - 9| - 5

• y = |x + 9| - 5

• y = |x - 9| + 5

• y = |x + 9| + 5

What is the final equation of a function that is vertically stretched by 2, shifted left 7 units, and down 6 units?

• y = 2|x + 7| - 6

• y = 2|x - 7| + 6

• y = 2|x - 7| - 6

• y = 2|x + 7| + 6