Today in Pre-Calculus

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

2. 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)

3. 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.

4. 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)

5. Example a When graphed, appears EVEN Algebraically: f(-x)=4(-x)2-1 = 4x2-1 =f(x)

6. Example b When graphed, appears ODD Algebraically:

7. Example c When graphed, appears Neither Algebraically: f(-x) = (-x)3+2(-x)2 = -x3+2x2 ≠ f(x) or –f(x)

8. Example d When graphed, appears ODD Algebraically: f(-x) = 2(-x)3-3(-x) = -2x3+3x =-(2x3-3x) =-f(x)

9. Example e When graphed, appears Neither Algebraically: f(-x) = -(-x)2+0.03(-x)+5 = -x2-0.03x+5 ≠ f(x) or –f(x)

10. Example f When graphed, appears Even Algebraically:

11. Homework • Wkst. • Quiz: Tuesday, September 22

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