Graphing Absolute Value Functions and Their Transformations

This video tutorial teaches how to graph absolute value functions with transformations. It covers the basic shape of the parent function, explains how transformations like shifting, stretching, and reflecting affect the graph, and provides three detailed examples. Each example demonstrates finding the vertex, applying transformations, and determining the domain and range of the function.

What is the basic shape of the parent function y = |x|?

• A straight line

• A V-shape

• A U-shape

• A circle

How does the graph of y = |x| change when you add a positive constant inside the absolute value bars?

• It shifts downwards

• It shifts upwards

• It shifts to the left

• It shifts to the right

What effect does a negative 'a' value have on the graph of an absolute value function?

• It reflects the graph over the x-axis

• It shifts the graph to the right

• It makes the graph wider

• It shifts the graph to the left

In the function y = |x + 1| - 3, where is the vertex located?

• (-1, -3)

• (1, 3)

• (1, -3)

• (-1, 3)

What is the range of the function y = |x + 1| - 3?

• y ≥ -3

• y ≤ -3

• y ≥ 3

• y ≤ 3

For the function y = -2|x - 3| + 4, what is the vertex?

• (3, -4)

• (-3, -4)

• (-3, 4)

• (3, 4)

What is the range of the function y = -2|x - 3| + 4?

• y ≥ 4

• y ≤ 4

• y ≥ -4

• y ≤ -4

In the function y = (1/3)|x + 1| - 2, what does the (1/3) value do to the graph?

• Makes the graph narrower

• Makes the graph wider

• Shifts the graph to the left

• Shifts the graph to the right

Where is the vertex of the function y = (1/3)|x + 1| - 2?

• (-1, 2)

• (1, -2)

• (1, 2)

• (-1, -2)

What is the range of the function y = (1/3)|x + 1| - 2?

• y ≤ 2

• y ≥ 2

• y ≤ -2

• y ≥ -2