Question

How do you find the domain and range for `y=x^2+3`?

Answer 1

Domain; `x in RR`
Range; `y>=3`

Explanation:

The domain for this function can be considered by considering what values of x make y be defined, and we see evidently that `x` can take on any real value as a simply porabola, with no asymptotes, and y would be defined; so hence `x in RR`

The range can be found by considering the graph of this equation, just `y=x^2` shifted 3 units upward;

graph{x^2+3 [-18.67, 21.33, -1.08, 18.92]}

So from this we see that `y` has the smallest value at 3, where `x=0` and otherwise is `>3`

hence `y` is always 3 or greater.

Hence yielding a range of; `y>=3`