Question

Question #32052

Answer 1

Domain: `(-oo, 0) uu (0, oo)`

Explanation:

You can easily see the domain (acceptable x-values) from the graph.
This graph is called a volcano. Even though it looks like it, the function never touches the y-axis `(x=0)` which is a vertical asymptote and it never touches the `y=-25` line since it is a horizontal asymptote.
graph{1/x^2 - 25 [-40.72, 40.4, -30.46, 10.14]}.

By default, the domain of a function is typically `(-oo, oo)`. When the function is a fraction with a variable in the denominator, you introduce vertical asymptotes -- locations where the function becomes undefined. Square root functions and trigonometric functions also change the domain.

In your example `x = 0` causes the undefined condition -- the vertical asymptote.