Today in PreCalculus Go over homework Notes Symmetry

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

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)

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.

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)

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

Example b When graphed, appears ODD Algebraically:

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

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

Example e When graphed, appears Neither Algebraically: f(-x) = -(-x)2+0. 03(-x)+5 = -x 2 -0. 03 x+5 ≠ f(x) or –f(x)

Example f When graphed, appears Even Algebraically:

Homework • Wkst. • Quiz: Tuesday, September 22

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