Question

How do you find the domain and range for `y = x^2-5`?

Answer 1

the domain is `RR`, the range is `[-5, +oo)`

Explanation:

Since y is a polynomial, its domain is `RR`

Then you find x:

`x^2=y+5`

that has two solutions:

`x=+-sqrt(y+5)`

that are verified only if `y+5>=0`

or `y>=-5`

Then the range of y is `[-5, +oo)`

You also can see the domain and the range in the graphic:

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

the domain, on x-axis, is all along the line,
the range begin in the y-coordinate -5 and continues to `+oo`