4.1 Power Functions and Models

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Presentation transcript:

4.1 Power Functions and Models

Examples of Power Functions:

The graph is symmetric with respect to the y-axis, so f is even. The domain is the set of all real numbers. The range is the set of nonnegative numbers. The graph always contains the points (-1,1), (0,0), and (1,1). As the exponent increases in magnitude, the graph becomes more vertical when x <-1 or x >1, but for x near the origin the graph tends to flatten out and lie closer to the x-axis.

(-1, 1) (1, 1) (0, 0)

The graph is symmetric with respect to the origin, so f is odd. The domain and range are the set of all real numbers. The graph always contains the points (-1,-1), (0,0), and (1,1). As the exponent increases in magnitude, the graph becomes more vertical when x > 1 or x <-1, but for x near the origin the graph tends to flatten out and lie closer to the x-axis.

(0, 0) (1, 1) (-1, -1)

Show each stage to obtain the graph of

(1,1) (0,0)

(0,0) (1, -2)

(1,0) (2,-2)

(1, 4) (2, 2)