Question

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

Answer 1

See below.

Explanation:

When finding the `"domain"` and `"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" = (-∞,∞)`