How would the graph of $y=(-1)^x$ look like?

Question

Question

When typing in $y=(-1)^x$ into a graphing calculator, it does not display anything at all. And once you think about it, you begin to realize that the f(x) values flip from positive to negative. How would this graph look like?

Answer 1

The expression $(-1)^x$ only has a (commonly accepted) meaning when $x$ is an integer.

If you plot the values of $(-1)^x$ for integer $x$, you get a sequence of points alternating between being $1$ unit above the $x$-axis and $1$ unit below.

      |
*     *     *     *     *     *
      |
------+-----------------------
      |
   *  |  *     *     *     *