# Question #32052

Feb 11, 2017

#### Answer:

Domain: $\left(- \infty , 0\right) \cup \left(0 , \infty\right)$

#### 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 $\left(x = 0\right)$ 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 $\left(- \infty , \infty\right)$. 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.