writing equations for piecewise functions and word problems chapter 2 day 2

Writing Equations for Piecewise Functions and

Word ProblemsChapter 2

Day 2

Writing a piecewise function Writing a piecewise function given the graph.given the graph.

The break in the graphIs at x=0.

To the left of x=0 the graph is part of the line thru (-2,0) & (0,2)

An equation of this line is:y = x + 2 y = x + 2

To the right of x=0, theGraph is part of the Line thru (0,0) & (2,2)

y = x +0y = x

Notice where the circle & dot are!!

The piecewise function is:The piecewise function is:

(open dot)

(closed dot)

0,

0,2)(

xifx

xifxxf

Steps to Writing Piecewise Steps to Writing Piecewise FunctionsFunctions

To find the equation of the line1. Find two points on the line2. Find slope3. Use point and slope in point slope form and

solve for yDo this for each line on the graphFind their boundary line, this is the number used in the

inequality

Open circle: <, >Closed Circle: <, >

4. Write the Piecewise function

Write the equation ofWrite the equation of

SolutionSolution

1,2

1

2

1

1,2

)(xifx

xifx

xf

ExampleExample

• You have a summer job that pays time and a half for overtime. (If you work more than 40 hours) After that it is 1.5 times your hourly rate of $7.00/hr.

1. Write and graph a piecewise function that gives your weekly pay P in terms of the number hours you work h.

2. How much will you make if you work 45 hours?

• From 0 to 40 hours you get $7.00/hr: 7h

• over 40 you get:

• 7(40) + (1.5)(7)(h-40) =

• 7(40) + 10.5(h-40)=

• 280 + 10.5h – 420 =

• 10.5h - 140

• The function is:

40,1405.10

400,7)(

hifh

hifhhP

So the graph is:

2. P(h) = 10.5h - 140

P(45) = 10.5(45) - 140

= $332.50 for 45 hours of work

ExampleExample1. Write and graph a

piecewise function for the parking charges shown on the sign.

2. What are the domain and range of the function?

SolutionSolution

Domain: 0 < t < 12Range: 3, 6, 8

Exit TicketExit TicketWrite a piecewise function for the given graph.