1. Pre-Calculus Section 1-3B Functions and Their Graphs

2. Graphing a Piecewise - Defined Function - Graph by hand (you can use the graphing calculator to guide you) - Use the domain portions to split the graph into parts (draw dashed vertical lines)

3. Need to remember the following graphs - line: y = mx + b - parabola: y = x 2

4. - absolute value: shape - square root: half parabola

5. Graph the Piecewise - Defined Function

8. Test for Even and Odd Functions A function is even if, for each x in the domain of f, f (-x) = f (x) So … 1.you replace all of the x’s with (-x)’s 2. evaluate the expression 3. if you “end up” with the original function the function is even

9. A function is odd if, for each x in the domain of f, f (-x) = - f (x) So … 1.you replace all of the x’s with (-x)’s 2. evaluate the expression 3. if you “end up” with the opposite of the original function the function is odd ( you normally have to factor a -1 out of the expression)

10. Determine if the function is even, odd, or neither. 4. g(x) = x 3 - x

11. Determine if the function is even, odd, or neither. 5. h(x) = x 2 + 1

12. Determine if the function is even, odd, or neither. 6. f(x) = x 3 - 1

13. Determine even or oddness graphically. Even Functions - are symmetric with respect to the y-axis (-x, y)  (x, y) Odd Functions - are symmetric with respect to the origin (-x, -y)  (x, y)

14. Use your graphing calculator to determine if the function is even, odd, or neither. 7. f(x) = 3x - 2

15. Use your graphing calculator to determine if the function is ever, odd, or neither. 8. g(x) = x 2 - 4

16. Use your graphing calculator to determine if the function is ever, odd, or neither. 9. h(x) = │x + 2│

17. Homework: Page 39 - 41 44 - 50 Evens 60 - 82 Evens 95 - 100 All