Question

What is the domain and range of `y = x^2 + 1`?

Answer 1

Domain: `x in RR`
Range: `y>=1`

Explanation:

The key realization here is that we have a polynomial here, which is defined for all real numbers, thus our domain is

`x inRR`

To think about the range, let's think about what the zero of this polynomial is:

`x^2+1=0`

`=>x^2=-1`

Notice, we will be taking the square root of a negative number here, which is undefined for real numbers.

If we set `y` equal to `1`, `x` will be zero, and our answer will always be positive as the number we add to `x^2` increases. Thus, our range is

`y>=1`

Hope this helps!