Question

How do you find the domain and range of `-x^2+7`?

Answer 1

Domain: `x in RR`
Range: `{y|y<=7}`

Explanation:

The domain is rather simple to figure out. Since the function is defined with real numbers for all `x`, the domain will be `x in RR`.

To figure out the range of the function, we'll consider it as a parabola. The leading term is negative so it'll be concave downwards (`nn`). This means that the domain is `-oo` to whatever the vertex of the parabola is.

The vertex of the parabola `y=x^2` is at `(0,0)` and our function is that same parabola, but translated `7` units up. This means the vertex will be at `(0,7)` and this means our range is `-oo` to `7`:
`{y|y<=7}`