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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