Graphing Piecewise Functions: Key Concepts and Examples

This video tutorial explains how to graph piecewise functions by breaking them into individual expressions and graphing each part separately. It covers graphing linear equations in slope-intercept form, handling overlaps, and managing critical points. The tutorial also demonstrates graphing functions with three pieces and applying inequalities to finalize the graphs. Key concepts include understanding piecewise functions, graphing techniques, and the importance of inequalities in defining function domains.

What is a piecewise function?

• A function defined by multiple equations over different intervals.

• A function that only has one variable.

• A function defined by a single equation.

• A function that is always linear.

What is the first step in graphing a piecewise function?

• Breaking it into individual expressions.

• Graphing the entire function at once.

• Finding the x-intercepts.

• Calculating the derivatives.

What is the y-intercept of the equation y = x + 4?

• -1

• 0

• 1

• 4

How do you represent a point that is not included in the graph?

• With a dashed line.

• With an open circle.

• With a filled circle.

• With a cross.

What does the slope of a line represent?

• The y-intercept.

• The length of the line.

• The steepness and direction of the line.

• The x-intercept.

In the equation y = -3, what is the slope?

• 1

• 0

• -3

• 3

How do you graph the equation y = 1/2x + 2?

• Start at y = 2 and use the slope 1/2 to go up 1 and right 2.

• Start at y = 0 and use the slope 1/2 to go up 1 and right 2.

• Start at y = 2 and use the slope 2 to go up 2 and right 1.

• Start at y = 1 and use the slope 1/2 to go up 1 and right 2.

What does an open circle on a graph indicate?

• The point is a minimum.

• The point is a maximum.

• The point is included in the graph.

• The point is not included in the graph.

What is the purpose of the vertical line test?

• To check if a graph is a function.

• To find the slope of a line.

• To determine the y-intercept.

• To calculate the area under the curve.

What is the key to graphing piecewise functions?

• Looking at each individual expression and its corresponding inequality.

• Ignoring the inequalities.

• Graphing all equations at once.

• Using only linear equations.