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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posted:7/11/2013
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Jun Wang Jun Wang Dr
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