Question

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

Answer 1

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

Explanation:

Finding the Domain
The domain is where the function is defined in terms of real numbers. This function is always defined, so the domain is all real numbers, `RR`.

Finding the Range
The range is the possible values that the function takes on. If we consider the function as a parabola, we can see that it will be concave downwards (`nn`) because of the negative leading coefficient

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