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Properties of Functions
Section 2.3 Properties of Functions
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N N E E V V E For an even function, for every point (x, y) on the graph, the point (-x, y) is also on the graph. So for an odd function, for every point (x, y) on the graph, the point (-x, -y) is also on the graph. Copyright © 2013 Pearson Education, Inc. All rights reserved
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Copyright © 2013 Pearson Education, Inc. All rights reserved
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Determine whether each graph given is an even function, an odd function, or a function that is neither even nor odd. Even function because it is symmetric with respect to the y-axis Neither even nor odd because no symmetry with respect to the y-axis or the origin. Odd function because it is symmetric with respect to the origin. Copyright © 2013 Pearson Education, Inc. All rights reserved
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Odd function symmetric with respect to the origin
Even function symmetric with respect to the y-axis Since the resulting function does not equal f(x) nor –f(x) this function is neither even nor odd and is not symmetric with respect to the y-axis or the origin. Copyright © 2013 Pearson Education, Inc. All rights reserved
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Practice: #35 g(x) = -3x2 – 5
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CONSTANT
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Where is the function increasing? From what x value to what x value?
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Where is the function decreasing? From what x value to what x value?
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Where is the function constant?
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b.) find domain and range
Practice: # 21. a.) find intercepts b.) find domain and range c.) Where is the graph increasing, decreasing, constant d.) Even, odd, or neither Copyright © 2013 Pearson Education, Inc. All rights reserved
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Copyright © 2013 Pearson Education, Inc. All rights reserved
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Copyright © 2013 Pearson Education, Inc. All rights reserved
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(e) List the intervals on which f is increasing.
(f) List the intervals on which f is decreasing. Copyright © 2013 Pearson Education, Inc. All rights reserved
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Copyright © 2013 Pearson Education, Inc. All rights reserved
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