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Algebra Success T1
LESSON 1: Piecewise and Step Functions
[Objective]
Students will explore the process of graphing piecewise and step functions under
specific conditions. Students will create piecewise function graphs and will describe,
interpret, and evaluate these functions for particular values.
[Prerequisite skills]
Coordinate graphing, graphing functions: linear, absolute value, square root, quadratic,
and constant, graphing inequalities
[Materials]
Student pages S1 – S16
Gridded index cards
Ruler
Scissors
Tape/glue
[essential que s t i O n s ]
1. What do the features of piecewise functions look like and how do we apply the
rules that define them?
2. What do the features of step functions look like and how do we apply the rules
that define them?
3. What are some real life situations that can be modeled using piecewise functions?
[WOrds FOr WOrd Wall]
Piecewise function, stepwise function, function table, condition, parameters,
scatter plot
[GrOuPinG]
Cooperative Pairs (CP), Whole Group (WG), Individual (I)
[levels O F teacher suPPOrt]
Modeling (M), Guided Practice (GP), Independent Practice (IP)
[MultiPle rePresentatiOns]
SOLVE, Graph, Algebraic Formula, Verbal Description, Graphic Organizer, Pictorial
Representation
[WarM-uP] (IP, I, WG) S1 (Answers are on T9.)
• Have students turn to S1 in their books to begin the Warm-Up. Students will
graph inequalities in preparation for the lesson on piecewise and step functions.
Monitor students to see if they need help during the Warm-Up. Have students
complete the problems and then review the answers as a class. {Algebraic Formula,
Graphs}
[hOMeWOrk]
Take time to go over the homework from the previous night.
[lessOn] [3 days (1 day = 80 minutes) (M, GP, IP, WG, CP, I)]
T2 Algebra Success
LESSON 1: Piecewise and Step Functions
SOLVE Problem (WG, GP) S2 (Answers on T10.)
Have students turn to S2 in their books. The first problem is a SOLVE problem. You
are only going to complete the S step with students at this point. Tell students that
during the lesson they will learn how to write and graph piecewise functions. They
will use this knowledge to complete this SOLVE problem at the end of the lesson.
{SOLVE, Verbal Description, Graphic Organizer}
Introduction to Piecewise Functions – Discovery Activity
(M, GP, CP, WG) S2, S3 (Answers on T10, T11.)
M, GP, CP, WG: Students will work in pairs, guided by the teacher, to
explore the features of a piecewise function. Students will
need gridded index cards (3 per pair), scissors and glue or
{Algebraic Formula, Verbal Description, Graph, Graphic
tape.
Organizer}
MODELING
Introduction to Piecewise Functions - Discovery Activity
Step 1: Have students work with a partner to complete the Function Table 1 on
S2 and plot the points on Card 1 for ƒ(x) = x + 2.
• Add the x and y axes and use a scale of 1.
• Put Card 1 aside for the next part of the activity.
y
5
4
3 y = x + 2
2
1
-5 -4 - - -
3 2 1 12345
- x
1
-2
-3
-4
-5
Algebra Success T3
LESSON 1: Piecewise and Step Functions
Step 2: Students can work with a partner to complete the Function Table 2 on S2
and plot the points on Card 2 for g(x) = 1.
• Add the x and y axes and use a scale of 1.
y
5
4
3
2 y = 1
1
- - - - -
5 4 3 2 1 12345x
-
1
-
2
-
3
-
4
-
5
• Put Card 2 aside for the next part of the activity.
Step 3: Students can work with a partner to complete Function Table 3 on S2 and
2
plot the points on Card 3 for h(x) = x .
• Add the x and y axes and use a scale of 1.
y
5
4
3
2 y = x2
1
-5 -4 -3 -2 -1 12345x
-1
-2
-3
-4
-5
• Put Card 3 aside for the next part of the activity.
T4 Algebra Success
LESSON 1: Piecewise and Step Functions
Step 4: Have students look at Card 1 and Function Table 1.
• What is the function of the line? f(x) = x + 2
-
• Given: f(x) is restricted to when x ≤ 1
• Have students draw a vertical line at negative one.
• What are the coordinate pairs that will fit the parameters of the
-
situation described by the condition of the restriction? ( 1, 1),
- - - - -
( 2, 0), ( 3, 1), ( 4, 2) Have students circle the points on the table on S2.
• Have students determine which side of the graph they will need.
(The left side)
• Have the students mark the left side with a 1 and cut the graph on
the vertical line. Have the students tape or glue Graph 1 in place on
S3.
y
1 5
4
3
2
1
- - - - -
5 4 3 2 1 12345
- x
1
-2
-3
-4 y=x+ 2
-5
Step 5: Have students look at Card 2 and Function Table 2.
• What is the function of the line? g(x) = 1
-
• Given: g(x) is restricted to when 1 < x < 1
• Have students draw a vertical line at negative one and positive one.
• What are the coordinate pairs that will fit the parameters of the
situation described by the condition of the restriction? (0, 1) Have
students circle the points on the table on S2.
• Have students determine part of the graph they will need. (The
middle section.)
• Have students cut the graph on the vertical lines. Have students
tape or glue Graph 2 in place on S3.
y 2
5
4 y = 1
3
2
1
- - - - -
5 4 3 2 1 12345
- x
1
-2
-3
-4
-5
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