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# 3_2 - Section 3.2 Power Functions and Models Instructor Ms...

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Section 3.2: Power Functions and Models Instructor: Ms. Hoa Nguyen 1 Graphs Power function of degree n : f ( x ) = ax n (1) a = 0: real number. n > 0: integer number. Figure 1: EVEN power If n is EVEN, f ( x ) = x n , then y = f ( x ) > 0 for every x . The graph is symmetric about the y -axis. The graph always contains (0 , 0), (1 , 1), ( - 1 , 1). the graph TOUCHes the x -xis only at the origin (0 , 0). Remark : When the EVEN exponent n increases, the graph becomes more vertical when x < - 1 or x > 1. the graph tends to flatten out and lie closer to the x -axis for x near the origin. 1

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Figure 2: ODD power If n is ODD, f ( x ) = x n , then y = f ( x ) > 0 when x > 0. y = f ( x ) < 0 when x < 0. The graph is symmetric about the origin. The graph always contains (0 , 0), (1 , 1), ( - 1 , - 1). the graph CROSSes the x -xis only at the origin (0 , 0). Remark : When the ODD exponent n increases, the graph becomes more vertical when x < - 1 or x > 1. the graph tends to flatten out and lie closer to the x -axis for x near the origin.
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