Alg 2 BC U7Day 5 – Function Operations
Function Notation:
f(x), read “f of x”, is the value of the function at a particular x value.
It is really just another name for ______.
Given , evaluate f(6), f(-2), f(15), and f(a).
Function Operations:
Addition
Multiplication
Subtraction
Division
Domains of sum/difference/product/quotient of functions: ______
** Special consideration for the domain of a quotient: ______
Example: Let f(x) = 3x + 8 and Find f + g and f – g and state their domains.
Example: Let f(x) = x2 – 1 and g(x) = x + 1. Find fg and and state their domains.
Acomposite functionis a combination of two functions such that the output for the first function becomes the input for the second function.
Composite Functions:
Example: Let f(x) = x – 2 and g(x) = x2.
a. Find and . b. Find and.
More Examples: Let , , , and .
a.) b.) c.)
d.) e.) f.)
Example: Suppose you are shopping in a store and have a coupon worth $5 off any item. At the same time, the store is having a sale where all items are discounted by 20%.
a. If x is the price of the item you wish to buy, write a function (call it f(x)) to represent the price after the $5 off coupon is applied.
b. If x is the price of the item you wish to buy, write a function (call it g(x))to represent price after the 20%discount.
c. Use a composition of your two functions (and call the composite h(x)) to model how much you would pay for an item if the salesperson applies the 20% discount first and then the $5 off coupon.
d. Use a composition of your two functions (and call the composite k(x)) to model how much you would pay foran item if the salesperson applies the $5 off coupon first and then the 20% discount.