This document discusses power functions and function operations in algebra 2. It defines power functions as having the form b^x where b is the base and integer exponents result in polynomial functions. It provides examples of adding, subtracting, multiplying, and composing various power functions, finding their domains. Students are assigned homework problems applying these concepts.

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)