1. 2.1 Graphs of Basic Functions and Relations; Symmetry

2. Quiz Fill in the blank below:
Given a function f is defined on I, if f increases on I, then for any x1<x2, f(x1)___f(x2)

3. Increasing, Decreasing and constant functions
Increasing function
Whenever x1<x2, f(x1)<f(x2)
Decreasing Function
Constant function
For every x1, x2, f(x1)=f(x2) y x y x y x

4. Basic Functions

5. Symmetry Symmetric WRT y axis y f(x) Symmetry WRT the y axis:
if (a,b) is on f(x), then (-a,b) is also on f(x)
Symmetry WRT the x axis:
if (a,b) is on f(x), then (a, -b) is also on f(x)
Symmetry WRT the origin:
if (a,b) is on f(x), then (-a,-b)is also on f(x) x
Symmetric WRT the origin
Symmetric WRT x axis

6. Even and Odd Functions
Even Function: f(x)=f(-x) for all x in the domain. Symmetric WRT the y-axis Odd Function: f(x)=-f(x) for all x in the domain. Symmetric WRT the origin

7. Testing Functions for Symmetry
f(x)=3x3-x
f(x)=x4-7x2+6
f(x)=x3-x+3

8. Homework
PG. 93: 18-75(M3)
KEY: 18, 30, 54, 66
Reading: 2.2 Vertical & Horizontal Shifts
Important due dates:
Feb. 11th Project 1
Feb. 14th Deadline for skilltest 1
Feb. 15th-16th Exam 1