Question

ptotic behavior of rational functions
provide your answer below:
as (x\to-infty,f(x)\tosquare.
as (x\to3^{+},f(x)\tosquare.)

Explanation:

Step1: Analyze \(x\to-\infty\)

Observe left - end behavior. As \(x\) goes to negative infinity, the function approaches the horizontal asymptote \(y = 2\).

Step2: Analyze \(x\to3^{+}\)

As \(x\) approaches \(3\) from the right, the function values increase without bound, so \(f(x)\to+\infty\).

Answer:

As \(x\to-\infty\), \(f(x)\to2\); As \(x\to3^{+}\), \(f(x)\to+\infty\)