how combining functions can be important to business, algebra homework help

Refer to the information on page 404 to explain how combining functions can be important to business. Describe how to write a new function that represents the profit, using the revenue and cost functions. What are the benefits of combining two functions into one function?

7-1
Operations on Functions
Main Ideas
• Find the sum,
difference, product,
and quotient of
functions.
• Find the composition
of functions.
GET READY for the Lesson
Carol Coffmon owns a store where
she sells birdhouses. The revenue
from birdhouse sales is given by
(x) = 125x. The cost of making
the birdhouses is given by
c(x) = 65x + 5400. Her profit p is
P=r- c. So the profit function p(x)
can be defined as p(x) = (v – c)(x).
the revenue minus the cost or
New Vocabulary
composition of functions
Arithmetic Operations Let f(x) and g(x) be any two functions. You can
add, subtract, multiply, and divide functions according to these rules.
Operations with functions
Examples if f(x) = x + 2. g(x) = 3x
KEY CONCEPT
Operation
Definition
(f + g)x) = f(x) + g(x)
Difference (4-9)(x) = f(x) – 9x)
Product (f.g)(x) = f(x) · g(x)
Sum
(x + 2) + 3x = 4x + 2
(x + 2) – 3x = -2x + 2
(x + 2)3x = 3×2 + 6x
f(x)
Quotient
96) 9(*) 0
x +
3x
***2*00
EXAMPLE Add and Subtract Functions
Given flx) = x2 – 3x + 1 and g(x) = 4x + 5, find each function.
a. (f+g)(x)
(+8)(x) = f(x) + g(x)
= (x2 – 3x + 1) + (4x + 5) 1x) = x2 – 3x + 1 and g(x) = 4x + 5
=x2+x+6
Simplity.
Addition of functions
Subtraction of functions
b. (f-g)(x)
(-3)(x) = f(x) – (x)
= (x2 – 3x + 1) – (4x + 5) x)=x2-3x + 1 and g(x) = 4x + 5
= x2 – 7x – 4
Simplify
CHECK Your Progress
Given flx) = x2 + 5x – 2 and g(x) = 3x – 2, find each function.
1A. (f+8)(x)
1B. (f-8)(x)