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2.1 Graphs of Basic Functions and Relations; Symmetry

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 x 1 <x 2 , f(x 1 )___f(x 2 ). Increasing, Decreasing and constant functions. y. x. y. x. y. x. Basic Functions. Symmetry.

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2.1 Graphs of Basic Functions and Relations; Symmetry

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  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 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

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