4.5 Graph Piecew ise Functions

4.5 Graph Piecewise Functions
CCSS
Content Standards
F.IF.4 For a function that models a relationship
between two quantities, interpret key features of
graphs and tables in terms of the quantities, and
sketch graphs showing key features given a verbal
description of the relationship.
F.IF.7.b Graph square root, cube root, and
piecewise-defined functions, including step functions
and absolute value functions.
2
Objective:
• Write and graph piecewise functions.
• Use piecewise functions to describe real-world
situations.
3
Example 1: Graphing Piecewise Functions
Graph: g(x) =
2x + 3
if x < 0
–2x + 3
if x ≥ 0
The domain is divided when x = 0, evaluate both parts of
the function at x = 0.
First part:
2(0) + 3 = 3
Plot: (0, 3) Open Circle (<)
●
O
●
●
Slope: 2
Second part:
–2(0) + 3 = 3
Plot: (0, 3) Closed Circle (≥)
Slope: –2
4
Example 2
Graph: f(x) =
4 if x ≤ –1
–2 if x > –1
The domain is divided when x = –1, evaluate both parts
of the function at x = –1.
First part:
4
Plot: (–1, 4) Closed Circle (≤)
●
Slope: 0 (Horizontal Line Left)
Second part:
–2
Plot: (–1, –2) Open Circle (>)
Slope: 0 (Horizontal Line Right)
O
5
Example 3
Graph: g(x) =
–3x
if x < 2
x+3
if x ≥ 2
The domain is divided when x = 2, evaluate both parts of
the function at x = 2.
First part:
–3(2) = –6
Plot: (2, –6) Open Circle (<)
●
Slope: –3
●
Second part:
2+3=5
Plot: (2, 5)
Slope: 1
●
Closed Circle (≥)
O
6
Example 4
Shelly earns $8 an hour. She earns $12 an hour for
each hour over 40 that she works. Sketch a graph
of Shelly’s earnings versus the number of hours
that she works up to 60 hours. Then write a
piecewise function for the graph.
Step 1 Make a table to organize the data.
Shelly’s Earnings
Hours
worked
Pay
($/hr)
0–40
8
>40
12
7
Example 4 Continued
Step 2 Determine the intervals for the function.
Shelly’s Earnings
Hours
worked
Pay
($/hr)
0–40
8
>40
12
0 ≤ h ≤ 40
equal to or less than 40 hours
h > 40
more than 40 hours
8
Example 4 Continued
Step 3 Graph the function.
Shelly earns $8 per hour for 0–40.
After 40 hours, she earns $12 per hour.
9
Example 4 Continued
Step 4 Write a linear function for each part.
0–40 hours: 8h
Use m = 8.
> 40 hours
Use m = 12
40 is the x and 320 is the y
320 = 12(40) + b
y = mx + b
320 = 480 + b
y = 12x – 160
-160 = b
The function is f(h) =
8h
12h – 160
if 0 ≤ h ≤ 40
if h > 40
10
Objective:
• Write and graph piecewise functions.
• Use piecewise functions to describe real-world
situations.
11

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