Graph a Piecewise-Defined Function

Writing Piecewise Functions from Graphs

By Melodie Hunt

Multiple Choice

Functions that are made up of distinct "pieces" of other functions defined over different intervals are called

• Absolute Value Functions

• Piecewise Functions

• Exponential Functions

• Quadratic Functions

Piecewise Function

Objective: to recognize the graph of a piecewise-defined function; to construct the graph of a piecewise-defined function; to manipulate the graphs of a family of piecewise-defined functions.

Writing a Piecewise Function Notation

Things to consider: 

How many pieces? 

What are the constraints on each piece? 

Will we need greater/less than/ equal to symbols?

What are the equations we need?

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Writing a Piecewise Function Notation

​Write a piecewise function for the graph to the right.

Solution 

• Two pieces

• Blue: horizontal line at 6, ends at x=0 (open dot)

• Gold: line with negative slope, inputs from 0 to 9 (one open, one closed dot) 

Multiple Choice

Graph

Multiple Choice

Match the graph with the correct equation.

Multiple Choice

Match the graph with the correct equation.

Multiple Choice

Match the graph with the correct equation.