Question #32052

1 Answer
Feb 11, 2017

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


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.