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Piecewise Functions (2.7)

Warm Up

#1. Evaluate f(x)=3x-2 when x = -2.

#2. Graph the lines –x+y=-2 and y = 1/3x – 2 on the same coordinate grid.

Piecewise Functions

Combination of equationsEach “piece” of the function corresponds to a

part of the domainEXAMPLE:

3x +2 is the function only when x < 3.x-1 is the function only when x > 3

3,1

3,23)(

xx

xxxg

Evaluating

Need to evaluate the function using the piece that contains the value of x in its domain:

Evaluate :a.) g(0) b.)g(10) c.) g(3) d.)g(-2)

3,1

3,23)(

xx

xxxg

Graphing a Piecewise Function

Pay attention to where the function changes The graph may or may not be connected where it changes

“pieces”

Example: Graph

3,1

3,23)(

xx

xxxg

Examples: Graph the following.

1. 2.

2,1

2,3

2

3

2)(

xx

xxxf

1,3

1,2)(

xx

xxxh

Step Function

Graph resembles steps

,4

,3

,2

,1

)(xf

01

12

23

34

x

x

x

x

Step Functions

Write a function for the graph below:

Writing a Piecewise Function

Write the equation for each piece of the function from the graph

Pay attention to the domain (where does the piece of the graph cover the x-axis?)

Be aware of solid vs. open circles

Example

Shipping costs $6 on purchases up to $50, $8 on purchases over $50 up to $100, and $10 on purchases over $100 up to $200. Write a piecewise function for these charges. Give the domain and range.

Example

A plane descends from 5000 ft at 250 ft/min for 6 min. Over the next 8 min, it descends at 150 ft/min. Write a piecewise function for the altitude A in terms of the time t. What is the plane’s altitude after 12 min?