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