Algebra 1
Lesson- Graphing Piecewise Functions
Name:____________________________________
Date:_____________________________________
Objective:
To learn how to graph piecewise functions.
Do Now: Graph: f ( x)  3x  2 for  3  x  0
y
x
Function Notation:
What is a piecewise function?
Examples:
Graph the following:
2 x if x  0
f ( x)  
2 if x  0
y
x
2 x  1 if x  0
g ( x)  
 x if x  0
y
x
1
Practice:
Graph the following:
1.
 3x  1 if x  1
f ( x)  
 4  x if x  2
y
2.
x  1 if x  0
f (x)  
 1 if x  0
y
x
3.
 1 if x  0

f ( x )   0 if x  0
  1 if x  0

y
x
4.
  x  1 if x  0

f ( x)  
5 if x  0
 x  2 if x  0

y
x
x
5.
 x  2 if x  1

f ( x )   2x if  1  x  1
  x if x  2

y
6.
 x  1 if x  1
f ( x)  
 x  2 if x  1
y
x
x
2
(1)
 x  1 if  1  x  0
f ( x)  
 x  1 if 0  x  1
y
(2)
x  2
f ( x)  
x  2
if x  1
if x  1
y
x
x
Graph each function, and state the domain and range in interval notation:
(3)
 x
f ( x)  
 x
if x  0
(4)
if x  0
x  3 if x  0
f ( x)  
 2x if x  0
y
y
x
x
Graph each function, and state the domain and range in interval notation:
3
(5)
 1 if x  0

f ( x )   0 if x  0
  1 if x  0

(6)
  x  1 if x  0

f ( x)  
5 if x  0
 x  2 if x  0

y
y
x
x
(7)
 x  2 if x  1

f ( x )   2x if  1  x  1
  x if x  2

(8)
 x  1 if x  1
f ( x)  
 x  2 if x  1
y
y
x
x
4
5
Algebra 2
Wkst: Graphing Piecewise Functions
Name:__________________________________
Date:___________________________________
1. Graph the following function:
x  2 if x  1
f ( x)  
 x  2 if x  1
y
x
2.
Graph the following function:
2 x  1 if x  0
g ( x)  
 x if x  0
y
x
6
Algebra 1
Lesson: Piecewise Models
Name:______________________________
Date:_______________________________
Objective:
(1)

write piecewise functions to model a situation
A beauty supply store sells eyeliner pencils for $4.00 each. For an order of 2 dozen or more pencils, the
price per pencil for all pencils ordered is reduced to $3.50. For an order of 5 dozen or more pencils, the
price per pencil for all pencils ordered is reduced to $3.25.
(a)
Ms. Ingram decides to go shopping and buys the following number of eyeliner pencils. Fill in the
chart to determine the total cost for each order she placed:
Number of
Pencils
10
24
42
59
60
Total
Cost
(b)
Write a piecewise function that relates the total cost in dollars for an order of x pencils.
(c)
Graph your piecewise function for 0  x  84.
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(2)
On weekends and holidays, Gunning Plumbing’s emergency plumbing repair service charges $2.00 per
minute for the first 30 minutes of a service call and $1.00 per minute for each additional minute.
(a)
Fill in the chart to determine the total cost for each call placed, given the number of minutes:
Time in
minutes
20
42
55
60
73
Total
Cost
(b)
Write a piecewise function P(t) which expresses the total cost of a service call in terms of time t in
minutes.
(c)
Using your function from part (b), how much would a 47 minute service call cost?
call?
A 75 minute
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Algebra 1
HW: Piecewise Models
Name:______________________________
Date:_______________________________
Objective:

write piecewise functions to model a situation
(1) In Exponential City, the system for speeding ticket fines is as follows:
Base Fine
$75.00
For speeds 1 – 5 MPH over the posted limit
$5 per MPH
For speeds 5 – 15 MPH over the posted limit
$5 per MPH (for the first five MPH)
$10 per each additional MPH
For speeds over 15 MPH over the posted limit
$5 per MPH (for the first five MPH)
$10 per MPH (for the next ten MPH)
$20 per each additional MPH
(a) Ms. Ingram often commutes on Function Highway, which goes through Exponential City. The
posted speed limit is 55 MPH. Fill in the chart to determine the total cost for each of the following
speeding tickets:
Recorded Speed
Cost of Ticket
58 MPH
61 MPH
70 MPH
50 MPH
(b) Write a piecewise function that relates the total cost in dollars for a speeding ticket in Exponential
City.
9
(2) A car rental agency charges $0.35 per mile if the total mileage does not exceed 50. If the total mileage
exceeds 50, the agency charged $0.35 for the first 50 miles plus $0.15 per mile for the additional mileage.
There is an additional charge of $100.00 for the total mileage that exceeds 100 miles.
Write the piecewise function that describes this situation.
(3) For a round trip ticket from Kalamazoo, Michigan to Walla Walla, Washington, a travel agency charged
$89 per person. In order to attract more clients, they offered the lower fare of $82 per person for bookings
of groups of more than 6 people, but less than 11 people. If 11 or more people booked for this trip, the fare
would be offered at $76 per person.
(a) Fill in the chart to determine the total cost for each group, given the number of people booked for the
flight:
People in Group
3
8
15
Total Cost
(b) Write a piecewise function that expresses the total cost of booking this flight.
(c) Graph this piecewise function and label the axes.
10