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What you will learn today1. How to evaluate piecewise functions2. How to graph piecewise functions3. How to determine piecewise functions from a graph
Objective: 2.7 Piecewise Functions
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Piecewise Functions
Up until this point, we have represented functions with one equation. In “real life” many situations can best be represented by a set of functions. Each function corresponds to a different part of the domain. These are called “piecewise functions”.
We are going to learn to evaluate piecewise functions, graph them and write them.
Objective: 2.7 Piecewise Functions
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Evaluating Example Evaluate f(x) when a) x = 0 b) x = 2, and c) x
= 4 given
212
22{)(
ifxx
ifxxxf
Objective: 2.7 Piecewise Functions
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You Try
Evaluate f(x) when a) x = 0, b) x = 3, c) x = 6
31
323{)(
ifxx
ifxxxf
Objective: 2.7 Piecewise Functions
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Graphing a Piecewise Function Graph
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12
3
2
1{)1(
ifxx
ifxxxf
Objective: 2.7 Piecewise Functions
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You Try Graph
31
323{)(
ifxx
ifxxxf
Objective: 2.7 Piecewise Functions
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A Step Function
A function that results in a graph that looks like a set of stairs. An example is the greatest integer function.
xxg )(
Objective: 2.7 Piecewise Functions
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Graphing a Step Function Graph
212
101{)(
xif
xifxf
434
323
xif
xif
Objective: 2.7 Piecewise Functions
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Writing a Piecewise Function Write an equation for the piecewise
function whose graph is shown.
Objective: 2.7 Piecewise Functions
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You Try Write an equation for the following
graph.
Objective: 2.7 Piecewise Functions
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A “Real World” Example You have a summer job that pays time and a half for overtime.
That is, if you work more than 40 hours per week, your hourly wage for the extra hours is 1.5 times your normal wage of $7. Write a piecewise function that gives you your weekly
pay P in terms of the number of hours you work. How much will you get paid if you work 45 hours?
Objective: 2.7 Piecewise Functions
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Homework Page 117, 14-20 even, 22, 26, 28, 38.
