Question

How do you find the domain of `y = x^2 - 7`?

Answer 1

In order to answer this question, you need to understand what a domain is, in mathematical terms.
A domain tells you all the possible values of x which make a certain equation/function true.

Explanation:

Because `y=x^2-7` is a quadratic equation, both positive and negative values of x will work (try substituting random numbers into the equation if you need proof).

With this in mind, you know that the graph of the function does not have any undefined points or any constraints.
That means there is an infinite number of solutions.

Therefore, the domain of `y=x^2-7` is simply...
`x=(-∞, ∞)` ---> interval notation
...or you can also say `x =`all real numbers.

I hope this helps a lot! :)