Question

Why can a cube root function have negative output values?

Answer 1

So let's start with the definition of cubed:

\[x^3=x*x*x\]

Answer 2

Notice that if 1 of your x's were negative, your output would be negative
If two of your x's were negative, then your output will be positive
If all three are negative, the your output is negative

Answer 3

this pattern continues forever.
Also, you should note that x has to be the same number: x=-1 for example means that

\[x^3=-1 \rightarrow x=\sqrt[3]{-1}\]

Answer 4

Or more clearly:

\[f(x)=x^3=x*x*x \rightarrow f(-1)=(-1)^3=(-1)*(-1)*(-1)=-1\]

Answer 5

does that make sense?

Answer 6

Yes! Thank you so much.

Answer 7

you're welcome