Exploring Absolute Value Functions as Piecewise Functions

This video tutorial explains how to express absolute value functions as piecewise functions. It begins with an introduction to piecewise functions and their characteristics. The tutorial then provides multiple examples, guiding viewers through identifying sections in graphs, determining the axis of symmetry, and writing equations for both upward and downward pointing graphs. The video emphasizes understanding slopes and y-intercepts in the context of piecewise functions.

What is a piecewise function?

• A function with two or more different sections of the graph.

• A function that only decreases.

• A function with a single linear equation.

• A function that only increases.

Where does the function change direction in an absolute value function?

• At the y-intercept.

• At the vertex.

• At the x-intercept.

• At the origin.

What is the first step in writing an absolute value function as a piecewise function?

• Draw the graph.

• Identify the value for the interval where the graph changes.

• Find the slope.

• Identify the y-intercept.

In the first example, what is the slope of the left side of the graph?

• 1

• -5

• -1

• 5

What is the y-intercept of the right side of the graph in the first example?

• 5

• -1

• 0

• -5

In the second example, what is the y-intercept of the left side of the graph?

• 4

• 6

• 2

• 8

What is the slope of the right side of the graph in the second example?

• -2

• 2

• -1

• 1

In the third example, what is the x-value of the axis of symmetry?

• 5

• 2

• 3

• 4

What is the slope of the left side of the graph in the fourth example?

• 1

• -1

• -2

• 2

What is the y-intercept of the right side of the graph in the fourth example?

• 12

• 10

• 8

• 6