Writing Equations for Piecewise Functions and Word Problems Chapter 2 Day 2

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

The piecewise function is: (open dot) (closed dot)

Steps to Writing Piecewise Functions To find the equation of the line 1. Find two points on the line 2. Find slope 3. Use point and slope in point slope form and solve for y Do this for each line on the graph Find their boundary line, this is the number used in the inequality Open circle: <, > Closed Circle: <, > 4. Write the Piecewise function

Write the equation of

Solution

Example

You have a summer job that pays time and a half for overtime 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. Write and graph a piecewise function that gives your weekly pay P in terms of the number hours you work h. 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:

So the graph is:

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

Example Write and graph a piecewise function for the parking charges shown on the sign. 2. What are the domain and range of the function?

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

Exit Ticket Write a piecewise function for the given graph.