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2.1 Graphs of Basic Functions and Relations; Symmetry.

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Presentation on theme: "2.1 Graphs of Basic Functions and Relations; Symmetry."— Presentation transcript:

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 x 1

3 Increasing, Decreasing and constant functions Increasing function Whenever x 1

4 Basic Functions

5 Symmetry x y f(x) Symmetric WRT y axis Symmetric WRT x axisSymmetric WRT the origin 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)

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)=3x 3 -x  f(x)=x 4 -7x 2 +6  f(x)=x 3 -x+3

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


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