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Operations
with Functions Including Composition
Designed by: Melanie B. Moorer
School: Dreher High School
Grade Level: 10
Subject: Mathematics (Algebra II)
Core
Curriculum Objective: Perform operations
with functions including compositions.
Overview: Students will work
independently and in small groups to develop
strategies to perform operations with
functions including compositions and apply
their knowledge in everyday situations.
Students will use various instructional
strategies such as: demonstrations, critical
thinking, and deduction. As a culminating
assessment, students will create five test
questions using two functions and performing
all operations including composition. The
students will submit the answers to their test
questions as a way of demonstrating their
mastery of the objective.
Purpose/Essential Question(s):
How do you perform operations with functions
including composition?
Time Frame: This lesson is designed for
one ninety-minute class period.
Resources
and Instructional Materials:
Algebra
II: An Integrated Approach,
D. C. Heath and Company
Lexington, Massachusetts / Toronto, Ontario
Pages 291-297
Transparencies
Overhead
Projector
Bell-Work: (work to be done when the
student enters the class before the tardy
bell)
Have
students do the following Warm-up exercises:
1.Evaluate
f(x) for the indicated values:
a.
f(x) = 5x + 3, for x = -5, 9
b.
f(x) = 8x - 1, for x = -1, 0
2.
Solve the following:
a.
x+3=0
b.
2x-4=6
Motivating the lesson:
Ask the students what they believe operations
with functions are. Also ask them what they
believe a composition is. Briefly explain to
them the importance of compositions and
operations, and tell the students that will
learn how to perform operations and
compositions.
Work
through the following teacher-led examples:
1.Use
f(x) = 3x and g(x) = x - 5 and find:
a.
f(x) + g(x)
b.
f(x) - g(x)
c.
f(x) * g(x)
d.
f(x) / g(x)
e.
f(g(x))
2. The regular price of a new Ford Mustang is
$18,500. The dealership advertised a factory
rebate of $2200 and a I 1% discount. Compare
the sale price obtained by subtracting the
rebate first, then taking the discount, with
the sale price obtained by taking the discount
first, then subtracting the rebate.
Activity
One:
Have students work independently on Worksheet
A for 15 minutes. Then let the students get
with their partner (already selected by the
teacher when designating collaborative pairs)
compare work and reach a consensus on what the
correct answers are. After another ten
minutes, randomly select student pairs to come
up and find distances on the overhead for the
class to see.
For
homework, give the students some problems
similar to those on Worksheet A.
Activity
Two:
Students should create possible test questions
where they come up with their own functions
and perform the operations and composition of
the two functions for five sets of functions.
The students should include the answers to
their possible test
questions. The teacher will evaluate the
culminating assessment with the following
rubric:
| Culminating
Activity |
Excellent
25-18 |
Acceptable
17-14 |
Unacceptable
13-0 |
| Actual
Functions Selected |
All
five sets of equations are functions |
Four
or three sets of equations are
functions |
Less
than three sets of equations are
functions |
| Operations
Performed Correctly |
All
five sets of functions have correct
operations |
Four
or three sets of functions have
correct operations |
Less
than three sets of functions have
correct operations |
| Compositions
Performed Correctly |
All
five sets of functions have correct
compositions |
Four
or three sets of functions have
correct compositions |
Less
than three sets of functions have
correct compositions |
| Calculations
are shown Neatly |
All
five sets of functions have
calculations shown neatly |
Four
or Three sets of functions have
calculations shown neatly |
Less
than three sets of functions have
calculations shown neatly |
Worksheet
A
(Click
here for an printable Acrobat version of the
worksheet)
Function
Operations and Composition
Name_____________________________________
Date
____________________
Perform all operations for each set of
functions.
1. f(x) = x + 2 and g(x) = 3x
2.
f(x) = 4x and g(x) = 5 - 6x
3. f(x) = 2x and g(x) = x - 4
4.
f(x) = 5x + 3 and g(x) 2x + 11
5. f(x) = 3x - 1 and g(x) = 2x + 7
6.
f(x) = 2x - 3 and g(x) =-1/2x + I
Find
f(g(x)) and g(f(x)) for each set of functions.
7. f(x) = 2x and g(x) = -3x
8.
f(x) = 5x and g(x) = 4x - 3
9.
f(x) = 2x - 5 and g(x) = 3x + 4
10.
f(x) = 3x - I and g(x) = 7 - 4x |
