The end behavior of a function refers to the way that the graph of the function approaches or tends towards as the input values approach positive or negative infinity.
In this case, the function f(x) = x^2 - 4 / x^2 - 9 can be rewritten as:
f(x) = (x^2 - 4) / (x^2 - 9)
As x approaches positive infinity, the value of x^2 approaches infinity, so the value of x^2 - 4 and x^2 - 9 both approach infinity. This means that the value of the function f(x) approaches 0 as x approaches positive infinity.
As x approaches negative infinity, the value of x^2 approaches infinity, so the value of x^2 - 4 and x^2 - 9 both approach infinity. This means that the value of the function f(x) approaches 0 as x approaches negative infinity.
Therefore, the end behavior of the function f(x) is that it approaches 0 as x approaches both positive and negative infinity.