Writing Equations for Piecewise Functions and Word Problems

Mr. Swartz

Writing a piecewise function 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:

0 ,

0 ,2)(

xifx

xifxxf

(open dot)

(closed dot)

Write the equation of:

1 ,21

21

1 ,2)(

xifx

xifxxf

• 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)=

• 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

Assignment