1. Writing Equations for Piecewise
Functions and Word Problems
Mr. Swartz

2. Writing a piecewise function given
the graph.
The break in the graph
Is 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, the
Graph is part of the
Line thru (0,0) & (2,2)
y = x +0
y = x
Notice where the circle & dot are!!

3. The piecewise function is:



≥
<+
=
0,
0,2
)(
xifx
xifx
xf
(open dot)
(closed dot)

4. Write the equation of:





−>−−
−≤+
=
1,
2
1
2
1
1,2
)(
xifx
xifx
xf

5. • 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?

6. • 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
hifh
hP

7. So the graph is:

8. 2. P(h) = 10.5h - 140
P(45) = 10.5(45) - 140
= $332.50 for 45 hours of work

9. AssignmentAssignment