Question

The end behavior of f(x)=(2+x^2)/(x^2-36) most closely matches which of the following:

Answer 1

The given function is
f(x) = (x² + 2) / (x² - 36)

The end behavior talks about where the function approaches as the value of the variable is varied.
As an example, when the value of x approaches positive infinity, the function also approaches positive infinity.
Another is that when the value of x approaches negative infinity, the function approaches positive infinity because the variables have an even exponent (2).
In between this behavior, there are also different characteristics of the function. There is an asymptote at x = 6 and -6.