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

1 Answer
Joseph C.
Mar 27, 2018

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" = (-∞,∞)

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