Understanding Absolute Value Functions

This video tutorial explains how to graph absolute value functions in the form y = |x - h| + k. It covers how the values of h and k affect the graph's position, shifting it horizontally and vertically. Two examples are provided: one with y = |x + 2| - 3, demonstrating a left and downward shift, and another with y = |x - 3| + 2, showing a right and upward shift. The video also illustrates how to determine the vertex of the graph and verify transformations using animations.

What is the general form of an absolute value function?

• y = x^3 + k

• y = ax^2 + bx + c

• y = mx + b

• y = |x - h| + k

What happens to the graph of an absolute value function when h is positive?

• It shifts left

• It shifts right

• It shifts up

• It shifts down

If the equation is y = |x + h|, what can be said about the value of h?

• h is negative

• h is undefined

• h is zero

• h is positive

What is the effect of a positive k on the graph of an absolute value function?

• The graph shifts down

• The graph shifts up

• The graph shifts right

• The graph shifts left

In the function y = |x + 2| - 3, what is the value of h?

• 2

• -3

• -2

• 3

For the function y = |x + 2| - 3, what is the value of k?

• 3

• 2

• -2

• -3

What is the vertex of the function y = |x + 2| - 3?

• (-2, 3)

• (2, 3)

• (2, -3)

• (-2, -3)

In the function y = |x - 3| + 2, what is the value of h?

• -2

• 2

• -3

• 3

For the function y = |x - 3| + 2, what is the value of k?

• 3

• -3

• -2

• 2

What is the vertex of the function y = |x - 3| + 2?

• (3, -2)

• (-3, -2)

• (3, 2)

• (-3, 2)