2.7 Piecewise Functions p. 114

Up to now, we’ve been looking at functions represented by a single equation. In real life, however, functions are represented by a combination of equations, each corresponding to a part of the domain. These are called piecewise functions.

One equation gives the value of f(x) when x ≤ 1 And the other when x>1

Evaluate f(x) when x=0, x=2, x=4 First you have to figure out which equation to use You NEVER use both X=0 This one fits Into the top equation So: 0+2=2 f(0)=2 X=2 This one fits here So: 2(2) + 1 = 5 f(2) = 5 X=4 This one fits here So: 2(4) + 1 = 9 f(4) = 9

Graph: For all x’s < 1, use the top graph (to the left of 1) For all x’s ≥ 1, use the bottom graph (to the right of 1)

x=1 is the breaking point of the graph. To the left is the top equation. To the right is the bottom equation.

Graph:

Step Functions

Graph :

2.7 (continued) Writing Equations for Piecewise Functions and Word Problems p. 115

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 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!!

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

Write the equation of:

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) (h-40)= 10.5h The function is:

So the graph is:

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

Assignment