1. PreCalculus Section 4.2 Perform operation on functions Like, numbers, functions can be added, subtracted, multiplied, and divided. The profit generated by the production and sale of x items can be found by subtracting the cost function C(x) from the revenue function R(x). If R(x) = 50x and C(x) = 15x + 200, find the profit function P(x). Find the profit generated from the sale of 350 items. Solution: P(x) = R(x) – C(x) P(x) = 50x – (15x + 200) P(x) = 35x – 200 P(350) = 35(350) – 200 = 12050 The profit is $12,050

2. If f(x) = 2x 2 + 7x – 11 and g(x) = 9x + 4 find: (f+g)(x) = (f-g)(x) = (f · g)(x) = (f / g)(x) = (2x 2 + 7x – 11) + (9x + 4 ) = 2x 2 + 16x -7 (2x 2 + 7x – 11) - (9x + 4 ) = 2x 2 - 2x -15 (2x 2 + 7x – 11) (9x + 4 ) = 18x 3 + 71x 2 - 71x -44 2x 2 + 7x – 11 x ≠ -4/9 9x + 4

3. Another operation that can be performed between functions is composition. The composition of f(x) and g(x) is denoted by either f(g(x)) or (f ° g)(x). If f(x) = 2x + 5 and g(x) = x 2 + 4 find: f(g(x)) g(f(x)) f(g(2)) 2(x 2 + 4) + 5 = 2x 2 + 8 + 5 = 2x 2 + 13 (2x+5) 2 + 4 = 4x 2 + 20x + 25 + 4 = 4x 2 + 20x + 29 2(2) 2 + 13 = 21

4. The height h (in ft above sea level) of a weather balloon at time t (in minutes) can be modeled by h = 500 + 200t. The temperature T (in degrees Fahrenheit) at a height h (in ft above sea level) can be modeled by T = 70 -.0075 h. Find the temperature of the balloon after 90 minutes.

6. Assignment Page 128 problems 2,3, 5-10, 20,22,24,27,28,31,34,36