Graphing Piecewise Functions: Using Constraints and Inequalities

This lesson teaches how to graph piecewise functions by leveraging knowledge of graphing other functions. It covers the use of open and closed circles in inequalities, defines piecewise functions, and explains how to graph each part of a piecewise function. The lesson also addresses common mistakes, such as not using constraints correctly, and concludes with a summary of the key points.

What type of circle is used on a graph to indicate that a point is included in the solution set?

• Closed circle

• Dashed circle

• Shaded circle

• Open circle

Which expression would you use for x = 0 in the given piecewise function?

• f(x) = 3x - 1

• f(x) = x^2

• f(x) = 2x

• f(x) = -x + 1

What is the y-intercept of the function f(x) = -x + 1?

• 0

• 1

• 2

• -1

When graphing f(x) = -x + 1 for x < -1, what type of circle is used at x = -1?

• Closed circle

• No circle

• Shaded circle

• Open circle

For the function f(x) = 2x, what type of circle is used at x = -1?

• Open circle

• Shaded circle

• Closed circle

• No circle

What is a common mistake when graphing piecewise functions?

• Plotting the wrong y-intercept

• Using the wrong slope

• Using both open and closed circles

• Ignoring the constraints

What does the final graph of a piecewise function represent?

• The intersection of all functions

• Only the first function

• Only the second function

• The union of all function parts