Question

What is the domain and range of `y=x^2+3`?

Answer 1

Domain is `RR`

Range is `<3;+oo)`

Explanation:

Domain of a function is a subset of `RR` where function value can be calculated. In this example there are no limitations for `x`. They would appear if there was for example a square root or if `x` was in the denominator.

To calculate the range you have to analyse the graph of a function:

graph{(y-x^2-3)(x^2+(y-3)^2-0.04)=0 [-8.6, 9.18, -0.804, 8.08]}

From this graph you can easily see, that the function takes all values greater han or equal to `3`.