Question

How do you find the domain of `f(x) = x^2+3`?

Answer 1

Find all possible values. In this case, there are no limits, thus, `"D":{x inRR}`.

Explanation:

A parabola will always have a domain of `{x inRR}`. This is because, if you look at a graph, there are no limits to the domain, unless provided context that restricts the domain.

graph{x^2 + 3 [-10, 10, -5, 5]}

As you can see, no matter how much you zoom out, there will always be an `x`-value.

EXTRA

The range however, will have a limit to the parabola function.

This is all dependent on the `c`-value.

If we get the parent function, `f(x)=x^2`, and graph it.

graph{x^2 [-10, 10, -5, 5]}

We can see that the only possible `y`-values are values above `y=0`. Thus, the range is `"R":{y inRR|0<=y}`.

Hope this helps :)