Solve the resulting problems if the given changes are made in the indicated examples of this section.

In Example 6, change the exponent to −1/3.

Data from Example 6

Plot the graph of the function y = 2x^1/3.
In obtaining points for the graph, we use (1/3) as the power when using the calculator. If your calculator does not evaluate powers of negative numbers, enter positive values for the negative values of x and then make the results negative. Because x^1/3 = ³√x, we know that x^1/3 is negative for negative values of x because we have an odd root of a negative number. We get the following table of values:

The graph, shown in Fig. 11.2, can also be displayed on a calculator.

X -3 y -2.9 -1 0 1 2 -2 -2.5 -2.0 3 0 2.0 2.5 2.9