Understanding Absolute Value Functions

The video tutorial explains the concept of absolute value, its notation, and how it always results in a positive number. It demonstrates plotting the parent function of absolute value by using both negative and positive values. The tutorial then covers transformations of absolute value functions, including shifts, stretches, and reflections, using parameters h, k, and a. An example is provided to illustrate these transformations, showing how to graph a specific transformed function with a negative slope, resulting in a downward opening V-shape.

What does the absolute value of a number represent?

• The square of the number

• The number itself

• The negative of the number

• The distance from zero

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

• A straight line

• A V shape

• A U shape

• A circle

How does the 'h' value in the function y = a|x - h| + k affect the graph?

• It shifts the graph up or down

• It shifts the graph left or right

• It stretches the graph vertically

• It reflects the graph over the x-axis

What is the effect of a positive 'k' value in the function y = a|x - h| + k?

• Reflects the graph over the x-axis

• Reflects the graph over the y-axis

• Shifts the graph up

• Shifts the graph down

In the function y = a|x - h| + k, what does the 'k' value control?

• Horizontal shift

• Vertical shift

• Vertical stretch

• Horizontal stretch

What happens to the graph of y = a|x| when 'a' is greater than 1?

• The graph shifts to the left

• The graph becomes narrower

• The graph shifts to the right

• The graph becomes wider

In the function y = a|x - h| + k, what does a negative 'a' value do to the graph?

• Shifts it down

• Shifts it up

• Reflects it over the x-axis

• Reflects it over the y-axis

How does the graph of y = a|x| change when 0 < a < 1?

• It shifts to the left

• It becomes wider

• It shifts to the right

• It becomes narrower

If the function is y = -2|x - 1| + 4, where is the vertex located?

• (-1, -4)

• (1, -4)

• (-1, 4)

• (1, 4)

What is the symmetry property of the graph of an absolute value function?

• Symmetric about the y-axis

• Symmetric about the origin

• No symmetry

• Symmetric about the x-axis