Lesson Plan

Graphing Piecewise Functions

Graph Piecewise Functions
Cesar E.
Classroom teacher
Voyages Preparatory
Elmhurst, NY
Show More
Objectives

Students will be able to...

1. Graph piecewise functions.

2. Evaluate function values.

3. Create a design.

4. Solve word problems involving piecewise functions.

Subjects
Math
Grades 9
All Notes
Teacher Notes
Student Notes

1 DO NOW

Each student must have their own laptop. Model the first number for the students to learn how to use the program in graphing.

Student Instructions

Go to www.desmos.com to graph the following equations. Draw a sketch and describe the graph like it’s a cut line, cut circle, cut parabola, cut absolute value, cut exponential, cut radical function.

  1. y = 2x + 3  if  {-2 < x ≤ 5}

 

 

 

 

 

 

 

 

  1. y = 2if { x > -3}

 

  1. y = x2 – 4    if { x > -5}

 

 

 

 

 

 

 

 

  1. y =     if { 0<x <10}

 

  1. y = -|2x + 3|  if { -4 < x < 8}

 

 

 

 

 

 

 

 

  1.    if { 0 < x < 3}

 

2 Individual Think

Let the students describe the difference between the two graphs. 

Student Instructions

 

 

  1. Use desmos.com to graph the sketch of y = 2x2  and y = 2x2  if { x ≤ 5}.

 

 

 

 

 

 

 

 

 

 

  1. What is the difference on the graph of the two equations? Explain.

 

 

 

 

 

 

 

 

 

Write down your partner’s idea.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3 Launch

Define a piecewise function.

Show one example on how to graph a piecewise function using desmos and how to evaluate function values.

Student Instructions

Graphing Piecewise Functions

 

What is a piece-wise function?

Example:

 

Example 1. Use desmos.com to graph the function.

  1. Graph the function:

                  f(x) =

                         
  1.                                              Find f(-5)  c) Find f(-1)  d)Find f(4)

STEPS

          

  1. Enter each function on desmos.com

 

   

 

 

 

 

 

 

  1. Create a table of values for each function based on the given domain.

   

 

 

 

 

 

 

 

 

 

  1. Graph the functions.

              

  1. Find the function values.

 

 

 

 

 

 

 

 

 

 

4 Practice

Provide students different piecewise functions to graph. 

Student Instructions

Graphing Piecewise Functions

Easy: Graph the following using desmos.com and find the function values.

 

1.

 

  1. Graph.

 

 

  1. Find f(-5)
  2. Find f(1)
  3. Find f(4)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Moderately Difficult:

 Graph the following using desmos.com and find the function values.

 

2.

 

  1. Graph.

 

  1. Find f(0)
  2. Find f(-7)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Challenge Question. (10 points)

 

  1. Graph the following using desmos.com. Show me the picture of the graph when done.

 

 

 

 

 

 

 

 

 

 

2.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5 extension

Let students create their own piecewise function that will produce an art design.

Student Instructions

Create your own piecewise function that will produce a creative design like the examples you see from desmos.com