The document summarizes chapters 5 and 8 from a math class, including reviewing linear and nonlinear functions, parent functions, exponential relationships, domain and range, and composition of functions. It provides examples of composing two functions, expressing composition functions as simpler functions, and writing an expression for a composition function given the inner and outer functions.

1. SI SESSION 9/11/2012 PEREZ MATH 107
CHAPTERS 5 AND 8
Review Mondayʼs quiz!
What makes a linear function linear?
What makes a function become nonlinear?
Parent functions and theyʼre basic forms. (Handout :)
Exponential relationships:
1. positive vs negative
2. odd vs even
3. roots and rationales
How does this affect the domain and range of a function?
Algebraically (donʼt just graph on a calculator, work it out!), find the domain AND
range of the given function: f(x)= x^(-3/2)
ACTIVITY: Composition Functions (Review Handout to take home :)

2. **Quick Review Over Composition Functions:
new input
new output
Compose the two functions:
A. f(u) = 5u² and u(x) = x+3
B. g(q) = 10+q² and q(w) = 1/w
C. f(b) = 2b² and b(t) = t+t²
Express the composition function as two simpler functions:
A. y = √(x²+1) ⥤ f(x) = x²+1 , g(x) = √x
B. y = 5(x - 2)³ ⥤ f(x) = (x - 2) , g(x) = 5x³
If f(x) = 3x²+2 , g(x) = x + 2 , and h(x) = (x -1)² +2, find:
A. f(g(x))
3 (x + 2)² +2
3 (x² + 4x + 4) + 2
3x² + 12x +12 +2
3x² + 12x + 14
B. g•h(x)
[(x - 1)² + 2] + 2
(x² - 2x + 1+2) + 2
(x² - 2x + 3) + 2
x² - 2x + 5
Write an expression for V(x), given V(t) = t⁻¹⁄(t +2) and t(x) = 2x.
V(x) = (2x)⁻¹ ╱(2x +2)
= 1╱[2x(2x +2)]
= 1╱(4x² + 4x)
= 1╱ [4x(x + 1)]