1. 4.1 Power Functions and Models

3. Examples of Power Functions:

4. 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.

5. (-1, 1)
(1, 1)
(0, 0)

7. 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.

8. (0, 0)
(1, 1)
(-1, -1)

10. Show each stage to obtain the graph of

11. (1,1)
(0,0)

12. (0,0)
(1, -2)

13. (1,0)
(2,-2)

14. (1, 4)
(2, 2)