This preview shows page 1. Sign up to view the full content.
Unformatted text preview: even function. 3
2
(−x , x 2 ) 1
2 1 y = x2 (x , x 2 )
x
12 Outline Symmetry Positive/Negative Increasing/Decreasing Maximum/Minimum The Diﬀerence Quotient Odd Functions Deﬁnition
Suppose f is a function from D into R. We say that f is odd if
any of the following are true.
1 y = f (x ) is symmetric about the origin. 2 If (x , y ) lies on the graph of f , then so does (−x , −y ). 3 f (−x ) = −f (x ) for all x ∈ D . Outline Symmetry Positive/Negative Increasing/Decreasing Maximum/Minimum The Diﬀerence Quotient Odd Functions Example
f (x )
y = x3 3
1 2 2 Discuss the function
f (x ) = x 3 .
Complete the graph of
an odd function. 1
2 1 1
1
2
3 2 x Outline Symmetry Positive/Negative Increasing/Decreasing Maximum/Minimum The Diﬀerence Quotient Symmetry Example
Determine whether the following functions are even, odd, or
neither.
1 f (x ) = x 5 − 5x . 2 g (x ) = x 2 + 3 x . 3 h(x ) = x 6 − 4x 4 + 8x 2 + 2x . Outline Symmetry Positive/Negative Increasing/Decreasing Maximum/Minimum The Diﬀerence Quotient Positive and Negative Values
Suppose f is a continuous function from D to R.
The zeros of f and the points where f does not exist divide D
into intervals where f is positive and intervals where f is
negative.
We need only check one point in each...
View
Full
Document
This note was uploaded on 02/10/2014 for the course MATH 1050 taught by Professor K.jplatt during the Spring '14 term at Snow College.
 Spring '14
 K.JPlatt
 Math, Algebra

Click to edit the document details