1. Algebra 2
7.3 Power Functions and Function Operations
What is a function?
The sum of two functions is a __________________________________...
What type of functions have we studied?
Power Functions
Have the form: ___________________________________
• b is the _____________________________
• If b is an integer, this is a ____________________________ function.
EX1: For f (x) = 2 ξ1/2 and g(x) = −6 ξ1/2 .
a) What is the domain of f(x) and g(x)?
b) Find f (x) + γ ( ξ) . What is the domain?
c) Find f (x) − γ ( ξ) . What is the domain?
EX2: For f (x) = 3ξ and g(x) = ξ1/ 4 .
a) Find the product. What is the domain?
b) Find the quotient. What is the domain?

2. Composition of Functions
One function
g(x)
Composing functions
g(x) f(x)
Composition of functions creates ____________________________________________.
Composition of functions can be written: __________________
• This is read “f of g of x”.
• It’s also written ( f og )( ξ)
EX3: Let f (x) = 3ξ−1 and g(x) = 2 ξ − 1 .
a) f ( g(x)) b) g ( f (x))
c) f ( f (x)) d) Find the domain a, b, and c.
HW p. 418 (28 – 35 all)