College Algebra, Chapter 3, 3.2, Section 3.2, Problem 74

A family of functions is given. In part (a) and (b) graph all the given members of the family in the viewing rectangle indicated. In part (c) state the conclusions that you can make from your graphs.

$\displaystyle f(x) = \frac{1}{x^n}$

a.) $\displaystyle n = 1, 3; [-3, 3]$ by $[-3, 3]$







b.) $\displaystyle n = 2, 4; [-3, 3]$ by $[-3, 3]$







c.) How does the value of $c$ affect the graph?

As the value of $n$ increases, the graph expands. Also when the value of $n$ is odd, the graph is symmetric to the origin. On the other hand, when the value of $n$ is even, the graph is symmetric to $y$-axis.