1.4 Graphing Piecewise Functions.notebook
1­4 Graphing Piecewise Functions
August 25, 2015
What is a piecewise function?
A function that is written using two or more expressions
I can...
Graph piecewise functions
Pass up worksheet from yesterday
Jun 7­9:49 AM
Jun 7­9:49 AM
Example 1:
Bad news... You will have to graphs these without your graphing calculator. There are a few ways to graph these. We will go over 2 ways, and you can pick which way you like better.
Graph the following piecewise function.
Step 1: separate your function into 2 different functions: y = x ­ 2 if x< ­1
y = x + 3 if x ≥ ­1
Step 2: Graph each line on the same coordinate plane, IN PENCIL:
y = x + 3 y = x ­ 2 m = 1
m = 1
b = ­2
b = 3
Step 3: Erase the parts of each line that are not supposed to be included.
an
y = x + 3 if x ≥ ­1
th
y = x ­ 2 if x < ­1
This means I only want this line graphed when it's points have x coordinates LESS THAN ­1. I have to erase all the other points on that line.
er
at
re
(­1, 2)
G
an
th
ss
Le
(­1, ­3)
This means I only want this line graphed when it's points have x coordinates GREATER THAN ­1. I have to erase all the other points on that line.
Step 4: If the end point is included in the graph (≤, ≥) it should be closed circle. If the end point is not included (<, >) it should be an open circle.
y = x ­ 2 if x < ­1
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y = x + 3 if x ≥ ­1
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Example 1: Method 2
Example 2:
y = x + 3 if x ≥ ­1
y = x ­ 2 if x< ­1
Slope = 1
Graph the following piecewise function.
Slope = 1
Less Than
Greater Than
Greater Than
Less Than
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Jun 7­9:49 AM
1
1.4 Graphing Piecewise Functions.notebook
Example 3:
Graph the following piecewise function.
Jun 7­9:49 AM
August 25, 2015
Example 4:
Graph the following piecewise function.
Jun 7­9:49 AM
2