Graphing Piecewise Functions: Key Concepts and Examples

This video tutorial teaches viewers how to graph piecewise functions through a series of examples. Starting with simpler functions and progressing to more complex ones, the video covers graphing techniques for linear and quadratic functions within piecewise contexts. The instructor provides detailed explanations and visual aids to help viewers understand the process. The video concludes with a practice problem for viewers to solve and encourages engagement through comments.

What will you be able to do by the end of this video?

• Solve quadratic equations

• Graph piecewise functions

• Evaluate integrals

• Differentiate functions

In the first problem, what type of functions are being graphed?

• Two quadratic functions

• A quadratic and a linear function

• Two linear functions

• Three different functions

What does a closed circle on a graph indicate?

• The function is undefined at that point

• There is an actual point at that location

• The function is continuous

• The function has a maximum at that point

For the second piecewise function, what is the y-intercept of the quadratic function?

• 2

• -3

• 0

• 1

When graphing the second piecewise function, what type of circle is used at x = 0 for the quadratic function?

• Open circle

• Both open and closed circles

• Closed circle

• No circle

In the third piecewise function, what is the slope of the line y = x - 2?

• 2

• -2

• -1

• 1

What is the y-intercept of the line y = -2x + 4 in the third piecewise function?

• -2

• 4

• 2

• -4

For the fourth piecewise function, what are the cutoff points?

• x = -2 and x = 2

• x = 0 and x = 5

• x = 1 and x = 4

• x = -3 and x = 3

In the fourth piecewise function, what is the y-intercept of the parabola x^2 - 1?

• 1

• 0

• 2

• -1

What should you do if you have any questions about the video content?

• Rewatch the video

• Ask in the comments

• Search online

• Ignore them