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

1 Answer
May 29, 2017

Answer:

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 :)