4. state the end behavior for the graph of f(x) = x / (x - 4).

Explanation:

Step1: Rewrite the function

Rewrite $f(x)=\frac{x}{x - 4}$ as $f(x)=\frac{x-4 + 4}{x - 4}=1+\frac{4}{x - 4}$.

Step2: Analyze as $x\to+\infty$

As $x\to+\infty$, $\frac{4}{x - 4}\to0$. So $f(x)\to1$.

Step3: Analyze as $x\to-\infty$

As $x\to-\infty$, $\frac{4}{x - 4}\to0$. So $f(x)\to1$.

Answer:

As $x\to+\infty$, $y\to1$; as $x\to-\infty$, $y\to1$.