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 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

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 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

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