# 21 Graphs of Basic Functions and Relations; Symmetry

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```					2.1 Graphs of Basic Functions and
Relations; Symmetry
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)
Increasing, Decreasing and constant
functions

y

Increasing
Whenever x1<x2, f(x1)<f(x2)
function                                        x

y
Decreasin
Whenever x1<x2, f(x1)<f(x2)
g
Function                                         x

y

Constant
For every x1, x2, f(x1)=f(x2)
function                                         x
Basic Functions
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
x   also on f(x)

Symmetry WRT the origin:
if (a,b) is on f(x), then (-a,-b)is
also on f(x)

Symmetric WRT the origin     Symmetric WRT x axis
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
Testing Functions for Symmetry
 f(x)=3x3-x
 f(x)=x4-7x2+6
 f(x)=x3-x+3
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

```
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 views: 1 posted: 7/11/2013 language: English pages: 8
Jun Wang Dr
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