Today in Pre-Calculus

1. Today in Pre-Calculus • Notes: (no handout) • Combining Functions Algebraically • Composition of Functions • Go over quiz • Homework

2. Combining Functions Algebraically • Let f and g be two functions with intersecting domains. Then for all values of x in the intersection, the algebraic combinations of f and g are defined by the following rules: • Sum: (f+g)(x) = f(x) + g(x) • Difference: (f-g)(x) = f(x) - g(x) • Product: (fg)(x)=f(x)g(x)

3. Example • Let f(x) = 3x3 + 7 and g(x) = x2 – 1. Find the: • Sum • Difference • Product • Quotient

4. Composition of Functions • Functions that are combined but not by using arithmetic operations • Combined by applying them in order (be careful!) • Letfandgbe two functions such that the domain of f intersects the range of g. The composition f of g, (f◦g)(x)=f(g(x)).

5. Example Let f(x) = x2 + 4x – 5 and g(x) = 2x – 3 • (f◦g)(x) = (2x-3)2 + 4(2x-3) -5 = 4x2 – 4x – 8 • (f◦g)(2) =0 • (g◦f)(x) = 2(x2 + 4x – 5) – 3= 2x2 + 8x – 13 • (g◦f)(2) =11 • (g◦g)(x) = 2(2x- 3) – 3= 4x - 9

6. Example • (s◦t)(x) = b)(s◦t)(2) = c) (t◦s)(x) = d) (s◦s)(x) = e) (t◦t)(x) =

7. Homework • Pg. 124: 1-17 odd, ignore the domain part of the directions