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Explain what happens to the graph of y = xn, where n is an even positive integer, as n increases. Describe changes for x between – 1 and 1 and for x greater than 1 or less than – 1. Explain why these changes happen.

Verified Answer :

The graph will get flatter from –1 to 1.As you raise a proper fraction to higher even powers, you get smaller values, so the y-values get closer to the x-axis.The graph will get closer to the y-axis, or narrower.As you raise values greater than 1 (or less than –1) to higher even powers, you get larger values, so the graph increases at a faster rate.

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Answer:

The graph will get flatter from –1 to 1. As you raise a proper fraction to higher even powers, you get smaller values, so the y-values get closer to the x-axis. The graph will get closer to the y-axis, or narrower. As you raise values greater than 1 (or less than –1) to higher even powers, you get larger values, so the graph increases at a faster rate.

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