Question

What is the range of the function

Answer 1

Answer:  $-\infty < y < \infty$ which is choice A

This is the set of all real numbers.

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Explanation:

If you were to graph this function, then it spans infinitely upward and infinitely downward as well. That means that we can land on any y value we want, and that's why the range is the set of all real numbers.

Another approach we could take is to swap x and y to get $x = \sqrt[3]{y+8}$ which solves to $y = x^3-8$ . This is the inverse of the original function your teacher gave you. Recall that the domain and range swap roles when going from the original function to the inverse. What this means is that because the domain of

Domain of inverse = set of all reals

Range of original = set of all reals