Download Section 1.5 Combinations of Functions

Section 1.5
17
Combinations of Functions
Course Number
Section 1.5 Combinations of Functions
Instructor
Objective: In this lesson you learned how to find arithmetic
combinations and compositions of functions.
Date
I. Arithmetic Combinations of Functions (Pages 51−53)
What you should learn
How to add, subtract,
multiply, and divide
functions
Just as two real numbers can be combined by the operations of
addition, subtraction, multiplication, and division to form other
real numbers, two functions f and g can be combined to create
new functions such as the
ssssssss
ssss sssssssssss ssss
ssss sss
s of f and g to create new functions.
The domain of an arithmetic combination of functions f and g
consists of . . .
sss ssss sssssss ssss sss ssssss ss sss sssssss
ss s sss ss ss sss ssss ss sss ssssssss ssssssssss sssss ss sss sssssss
sssssssssss ssss ssss s ss
Let f and g be two functions with overlapping domains.
Complete the following arithmetic combinations of f and g for all
x common to both domains:
ssss s ssss
s
1) Sum: ( f + g )( x) =
2) Difference:
3) Product:
4) Quotient:
( f − g )( x) =
( fg )( x) =
⎛f ⎞
⎜⎜ ⎟⎟(x) =
⎝g⎠
ssss s ssss
ssss s ssss
s
s
ssss s sssss ssss s s
s
To use a graphing utility to graph the sum of two functions, . . .
sssss sss sssss ssssssss ss ss sss sssss sss ssssss ssssssss ss sss
ssssss ss ss ss s sss ssss sssss sss
Example 1:
Let f ( x) = 7 x − 5 and g ( x) = 3 − 2 x . Find
( f − g )(4) .
ss
Larson/Hostetler/Edwards Precalculus with Limits: A Graphing Approach, Fifth Edition Student Notetaking Guide
Copyright © Houghton Mifflin Company. All rights reserved.
18
Chapter 1
II. Compositions of Functions (Pages 53−56)
The composition of the function f with the function g is
( f D g )( x) =
sssssss
.
Functions and Their Graphs
What you should learn
How to find
compositions of one
function with another
function
For the composition of the function f with g, the domain of
f D g is . . .
sss sss ss sss s ss sss ssssss ss s ssss ssss ssss
ss ss sss ssssss ss ss
Example 2:
Let f ( x) = 3 x + 4 and let g ( x) = 2 x 2 − 1 . Find
(a) ( f D g )( x) and (b) ( g D f )( x) .
sss ssss s sss s ss
sss sss s s
III. Applications of Combinations of Functions (Page 57)
The function f ( x) = 0.06 x represents the sales tax owed on a
purchase with a price tag of x dollars and the function
g ( x) = 0.75 x represents the sale price of an item with a price tag
of x dollars during a 25% off sale. Using one of the combinations
of functions discussed in this section, write the function that
represents the sales tax owed on an item with a price tag of x
dollars during a 25% off sale.
What you should learn
How to use combinations
of functions to model and
solve real-life problems
ss sssss s ss sssss s ssssss
Additional notes
Homework Assignment
Page(s)
Exercises
Larson/Hostetler/Edwards Precalculus with Limits: A Graphing Approach, Fifth Edition Student Notetaking Guide
Copyright © Houghton Mifflin Company. All rights reserved.