a. Suppose $f(x)=\frac{1}{x}$. As $x \rightarrow \pm \infty, f(x)$ behaves like:
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Preview

Step 1 ：Suppose the function is \(f(x)=\frac{1}{x}\).

Step 2 ：As \(x\) approaches positive or negative infinity, the value of \(f(x)\) will approach 0.

Step 3 ：This is because as \(x\) becomes larger and larger (either in the positive or negative direction), the fraction \(\frac{1}{x}\) becomes smaller and smaller.

Step 4 ：We can illustrate this behavior by plotting the function \(f(x)=\frac{1}{x}\) for a range of \(x\) values.

Step 5 ：The plot of the function \(f(x)=\frac{1}{x}\) confirms our initial thought. As \(x\) approaches positive or negative infinity, the value of \(f(x)\) approaches 0.

Step 6 ：This is evident from the fact that the graph of the function gets closer and closer to the x-axis (where \(y=0\)) as \(x\) moves away from 0 in either the positive or negative direction.

Step 7 ：\(\boxed{\text{Final Answer: As } x \rightarrow \pm \infty, f(x) \text{ behaves like } y=0}\)