section 2.5 The Graph of a Function

# We need only check one point in each interval to

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Unformatted text preview: interval to determine where f is positive and where f is negative. Example Determine where f is positive and where f is negative. 1 2 3 Graph f (x ) = x 3 − 2x 2 − 4x + 8 and use the graph to determine the intervals on which f (x ) is positive and the intervals on which f (x ) is negative. f (x ) = x 3 − x . x g (x ) = . x −1 Outline Symmetry Positive/Negative Increasing/Decreasing Maximum/Minimum The Diﬀerence Quotient Increasing/Decreasing/Constant Deﬁnition Suppose f is a function from D into R. Suppose I is an interval in D. 1 f is increasing on I if x1 , x2 ∈ I with x1 < x2 imply f (x1 ) < f (x2 ). 2 f is decreasing on I if x1 , x2 ∈ I with x1 < x2 imply f (x1 ) > f (x2 ). 3 f is constant on I if x1 , x2 ∈ I implies f (x1 ) = f (x2 ). Outline Symmetry Positive/Negative Increasing/Decreasing Maximum/Minimum The Diﬀerence Quotient Examples. Example 1 Determine the intervals on which the function f graphed below is increasing/decreasing. 2 Discuss the end behavior of the function f graphed below. f (x ) 4 y = f (x ) 3 2 1 -3 -2 -1 1 2 3 4 x Outline Symmetry Positive/Negative Increasing/Decreasing Maximum/Minimum The Diﬀerence Quotient Maximum/ Minimum Values Deﬁnition Suppose f is a function from D into R. 1 A global maximum for f on...
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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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