section 2.5 The Graph of a Function

# Complete the graph of an even function 3 2 x x 2 1 2

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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 + 2|x |. 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...
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## 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.

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