How to Graph a Piecewise Function

The video tutorial explains how to graph piecewise functions by breaking down the process into steps. It covers rewriting expressions in y=mx+b form, identifying slopes and y-intercepts, and applying constraints to graph each segment. The tutorial demonstrates graphing three different lines with specific constraints, emphasizing the importance of shading only the valid parts of the graph.

What is a piecewise function primarily characterized by?

• A single linear equation

• Multiple expressions with constraints

• A quadratic equation

• An exponential function

When rewriting expressions in the form y = mx + b, what does 'm' represent?

• The slope

• The x-intercept

• The constant term

• The y-intercept

For the expression y = -1, what is the slope?

• 1

• 0

• -1

• Undefined

In the graph of y = 2x, what is the y-intercept?

• 2

• 0

• 1

• -2

What type of circle is used to represent x ≤ 0 in the graph?

• Closed circle

• Open circle

• No circle

• Dashed circle

For the expression y = 6, when is it valid according to the constraints?

• When x ≤ 3

• When x = 3

• When x > 3

• When x < 3

What is the purpose of erasing parts of the graph in a piecewise function?

• To make the graph look cleaner

• To adjust the scale of the graph

• To remove parts that do not meet the constraints

• To highlight the important parts