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**2.1 Graphs of Basic Functions and Relations; Symmetry**

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**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)

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**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

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Basic Functions

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**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

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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

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**Testing Functions for Symmetry**

f(x)=3x3-x f(x)=x4-7x2+6 f(x)=x3-x+3

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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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