# How do you find the domain and range of f(x) = x^3 + 5?

Mar 27, 2018

See below.

#### Explanation:

When finding the $\text{domain}$ and $\text{range}$ of a graph or equation, we look at all the accepted values of $x$ and $y$, respectively.

If we wanted to, we could graph this equation, and look to see where there is a value for each $x$ and $y$ value:

graph{x^3+5 [-17.76, 18.29, -4.18, 13.84]}

If we were to keep zooming and zooming out, we could see that there is a point somewhere in respect to each value on the $x$ and $y$ axis.

To do this without a graph, all we need to do is figure out if there are any numbers that would make this equation false. Luckily for us, there is not a number that disproves it.

We can check by continuously plugging in numbers for $x$, and getting an answer out for $y$.

So in the end, we know:

"Domain" = (-∞,∞)

"Range" = (-∞,∞)