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

y=1
y=-18
y=2
y=0
I still don't get this based on steve's answer will someone please help?

see the further discussion on your earlier post.

To determine the end behavior of the function f(x) = (2 + x^2)/(x^2 - 36), we can analyze what happens to the function as x approaches positive and negative infinity.

First, let's simplify the function. We can factor the denominator (x^2 - 36) as (x - 6)(x + 6). Thus, the function can be written as:

f(x) = (2 + x^2)/((x - 6)(x + 6))

As x approaches positive or negative infinity, we can ignore the constant term "2" and simplify the function to:

f(x) ≈ x^2/((x - 6)(x + 6))

Now, let's analyze the behavior of the function as x approaches positive and negative infinity:

1. As x approaches positive infinity:
- In this case, we can see that x^2 will dominate the denominator because it increases without bound. The terms (x - 6) and (x + 6) will be relatively insignificant compared to x^2.
- Therefore, we can approximate the function as f(x) ≈ (x^2)/(x^2) = 1.
- So, as x approaches positive infinity, the end behavior of the function f(x) is y = 1.

2. As x approaches negative infinity:
- Similar to the case above, as x approaches negative infinity, x^2 dominates the denominator, and the terms (x - 6) and (x + 6) become insignificant.
- Thus, we can approximate the function as f(x) ≈ (x^2)/(x^2) = 1.
- As x approaches negative infinity, the end behavior of the function f(x) is also y = 1.

Based on the above analysis, the end behavior of the function f(x) = (2 + x^2)/(x^2 - 36) most closely matches y = 1.

It's important to note that Steve's answer may not have been clear or lacked sufficient explanation, so it's good to seek further clarification. If you have any additional questions, feel free to ask!