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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