This document provides examples of graphing composite functions. It explains that to find the domain of a composite function f(g(x)), you must consider the restrictions on the domains of both the inner and outer functions. It then gives three examples of determining the composite functions f(g(x)) and g(f(x)) for various functions f and g, and calculating or graphing their domains and ranges. The final example asks to determine possible functions f and g that satisfy three given composite functions.

1. Problem of the Day

2. Graphing Composite Functions
Warm-up
Consider f(x) = √x and g(x) = -x2 + 2x
Determine (f(g(x)) and (g(f(x))
To find the domain of (f(g(x)) you must consider
the restrictions on the domain of g(x) and the new
restrictions for (f(g(x))

3. 1
Ex 1) Consider f(x) = x + 3 and g(x) = x2 - 4x
Determine (f(g(x)) and (g(f(x)) and state its domain.

4. Ex 2) Let f(x) = x + 1 and g(x) = x2. Sketch a graph of
each composite function below and state its
domain and range.
a) y = f(g(x))
b) y = g(f(x))
c) y = f(f(x))
d) y = g(g(x))

6. Ex 3) Determine possible functions f and g so that:
a) f(g(x)) = (x - 2)2
b) f(g(x)) = √x + 3
c) f(g(x)) = x2 + 4x + 3

7. Assignment:
p.314 #3, 4, 5, 6, 7ac