1. 7.3 Power Functions & Function Operations p. 415

2. Sum :f(x) + g(x) = (f+g)(x) Difference :f(x) - g(x) = (f-g)(x) Product :f(x) * g(x) = (fg)(x) Quotient :

3. f(x) = 2x – 3 and g(x) = Sum Difference Product Quotient

4. INPUT (DOMAIN) OUTPUT (RANGE) FUNCTION MACHINE In order for a relationship to be a function… EVERY INPUT MUST HAVE AN OUTPUT TWO DIFFERENT INPUTS CAN HAVE THE SAME OUTPUT Functions ONE INPUT CAN HAVE ONLY ONE OUTPUT

5. Look on page 67 No two ordered pairs can have the same first coordinate (and different second coordinates).

6. 1 2 3 4 6 5 9 10 12 15 13 1 2 3 4 5 6 7 8 11 14 Time of DayDegrees C Domain Inputs: 1,2,3,4,5,6 Contains the Range Outputs: 9,10,12,13,15

7. {(2,5), (3,8), (4,6), (7, 20)} {(1,4), (1,5), (2,3), (9, 28)} {(1,0), (4,0), (9,0), (21, 0)} Ex.

8. “f of x” Input = x Output = f(x) = y Notation

9. Ex: Let f(x)=3x 1/3 & g(x)=2x 1/3. Find (a) the sum, (b) the difference, and (c) the domain for each. (a)3x 1/3 + 2x 1/3 = 5x 1/3 (b)3x 1/3 – 2x 1/3 = x 1/3 (c)Domain of (a) all real numbers Domain of (b) all real numbers

10. Ex: Let f(x)=4x 1/3 & g(x)=x 1/2. Find (a) the product, (b) the quotient, and (c) the domain for each. (a)4x 1/3 * x 1/2 = 4x 1/3+1/2 = 4x 5/6 (b) = 4x 1/3-1/2 = 4x -1/6 = (c) Domain of (a) all reals ≥ 0, because you can’t take the 6 th root of a negative number. Domain of (b) all reals > 0, because you can’t take the 6 th root of a negative number and you can’t have a denominator of zero.

11. Evaluate (f-g)(x) when x = 2 for the functions (f - g)(x) = (f - g)(2) =

12. Composition f(g(x)) means you take the function g and plug it in for the x-values in the function f, then simplify. g(f(x)) means you take the function f and plug it in for the x-values in the function g, then simplify.

13. The COMPOSITION of the function f with g is Plug the second function into the first

14. Evaluate the following when x = 0, 1, 2, 3 given that

15. Ex: Let f(x)=2x -1 & g(x)=x 2 -1. Find (a) f(g(x)), (b) g(f(x)), (c) f(f(x)), and (d) the domain of each. (a) 2(x 2 -1) -1 = (b) (2x -1 ) 2 -1 = 2 2 x -2 -1 = (c) 2(2x -1 ) -1 = 2(2 -1 x) = (d) D DD Domain of (a) all reals except x=±1. Domain of (b) all reals except x=0. Domain of (c) all reals except x=0, because 2x-1 can’t have x=0.

17. Journal When I hear someone say “Math is Fun” I… –5 sentences minimum

18. Assignment