Last Night’s HW  6. no  8. yes  32a. 2  32b. 5  32c. √x+2  33a. -1/9  33b. undefined  33c. 1/(y^2 + 6y) 66. D: (- ∞, 0) U (0, 2) U (2, ∞) 68. D: (-6, ∞) 70. D: (- ∞, -3) U (3, ∞)

Essential Question  How do you determine the relative max, min, intervals of increase, decrease, even and odd functions?

1.2 Graphs of Functions  Example 1: Given the graph shown, answer the following questions? a) What is f(0) ? b) What is f(9)? c) What is the domain? d) What is the range? e) What are the x-intercepts? f) How often does the line y = -1 intercept the graph? a. f(0)=-3 (-4, 2) (-2, 0) (0, -3) (1, -2) (3, 0) (5, 4) (7, 0) (9, -2) (10, -1) b. f(9)=is undefined c. D=[-4, 9) U (9, 10) d. R=[-3, 4] e. (-2, 0), (3, 0), (7, 0) f. 4 times

Increasing and Decreasing Functions Decreasing Constant Increasing

Example 2: Determine the open intervals on which each function is increasing, decreasing, or constant. a. b. c. (-1, 2) (1, -2) f(x) = x 3 - 3x (0, 1) (2, 1) Increasing: (-∞,∞) Increasing: (-∞, -1) U (1,∞) Decreasing: (-1, 1) Increasing: (-∞, 0) Constant: (0, 2) Decreasing: (2, ∞)

Relative Max and Min Values Relative Max Relative Min

Example 3: Use a graphing utility to approximate the relative maximum/minimum of the functions Sol: Min (0.67, -3.33) f(x) = 3x 2 - 4x - 2 a) f(x) = 3x 2 - 4x - 2b) f(x) = -x 3 +x Sol: Min (-0.58, -0.38) Max (0.58, 0.38)

Khan Academy  Recognizing Odd and Even Functions  Connection between even and odd numbers and functions

Even and Odd Functions: Graphically Even Function Symmetric to y-axis Odd Function Symmetric to origin Not a Function: Symmetric to x-axis

Even and Odd Functions: Algebraically Even Function: A function f is even if, for each x in the domain of f, f(-x) = f(x). Odd Function: A function f is odd if, for each x in the domain of f, f(-x) = -f(x) Example 7: Determine whether each function is even, odd or neither. EVEN ODD EVEN NEITHER

Homework  Pg96  #1-6all, #13-18 all, 21,22, 48, 50