1. Today in Pre-Calculus Go over homework Notes: Symmetry –Need a calculator Homework

2. 1.Vertical: x = -3 Horizontal: none 2.Vertical: x =-2, x = 2 Horizontal: y=0 3.Vertical: x = 3 Horizontal: y =0

3. Symmetry Symmetry with respect to the y-axis. These are EVEN functions Their graphs appear the same on both sides of the y-axis. Algebraically for every x in the domain of f, f(-x)=f(x)

4. Symmetry Symmetry with respect to the x-axis. Note: These are NOT functions Their graphs appear the same on both sides of the x-axis. Algebraically for every (x,y) on the graph (x,-y) is also on the graph.

5. Symmetry Symmetry with respect to the origin These are ODD functions Their graphs appear the same on both sides of the origin. Algebraically for every x in the domain of f, f(-x)=-f(x)

6. Example a When graphed, appears EVEN Algebraically: f(-x)=4(-x) 2 -1 = 4x 2 -1 =f(x)

7. Example b When graphed, appears ODD Algebraically:

8. Example c When graphed, appears Neither Algebraically: f(-x) = (-x) 3 +2(-x) 2 = -x 3 +2x 2 ≠ f(x) or –f(x)

9. Example d When graphed, appears ODD Algebraically: f(-x) = 2(-x) 3 -3(-x) = -2x 3 +3x =-(2x 3 -3x) =-f(x)

10. Example e When graphed, appears Neither Algebraically: f(-x) = -(-x) 2 +0.03(-x)+5 = -x 2 -0.03x+5 ≠ f(x) or –f(x)

11. Example f When graphed, appears Even Algebraically:

12. Homework Wkst. Quiz: Thursday, September 18