Understanding Absolute Value Functions

This video tutorial explains how to graph an absolute value function that involves reflection and translation. It begins by comparing the basic absolute value function y = |x| with its reflection across the x-axis. The tutorial then introduces the standard form of an absolute value function and explains how parameters a, h, and k affect the graph. The video demonstrates graphing transformations using animations and manual methods, and verifies the results using tables and graphing software.

What is the primary focus of this video tutorial?

• Graphing linear functions

• Graphing quadratic functions

• Graphing absolute value functions

• Graphing exponential functions

How do the y-values of the basic absolute value function compare to its reflection?

• They are identical

• They are the negatives of each other

• They are doubled

• They are halved

What does the parameter 'a' indicate in the standard form of an absolute value function?

• Rotation

• Reflection and stretch/compression

• Vertical shift

• Horizontal shift

If 'h' is negative in the function y = a|x - h| + k, what does it imply?

• Shift to the right

• Shift to the left

• Shift upwards

• Shift downwards

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

• Shift to the right

• Shift to the left

• Shift upwards

• Shift downwards

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

• (2, 3)

• (2, -3)

• (-2, 3)

• (-2, -3)

What is the first step in graphing the transformed function by hand?

• Sketching the parent function

• Plotting the vertex

• Shifting the graph

• Reflecting across the x-axis

How can you verify the accuracy of your graph?

• By guessing

• By checking with graphing software

• By using a calculator

• By asking a friend

What is the slope of the graph to the right of the vertex?

• Zero

• Undefined

• Negative one

• Positive one

What is the purpose of completing a table of values?

• To find the x-intercepts

• To calculate the range

• To verify the graph

• To determine the domain