The image you uploaded presents a function $y = f(x)$ graph and asks to analyze the behavior of $f(x)$ as $x$ approaches various limits.

Here's a breakdown based on the graph and provided options:

1. (a) As $x \to -\infty$, $f(x) \to$

   • Observing the left side of the graph (as $x \to -\infty$), the function $f(x)$ appears to approach zero from the positive side.
   • Answer: $0$.

2. (b) As $x \to 1^-$, $f(x) \to$

   • As $x$ approaches 1 from the left ($x \to 1^-$), $f(x)$ sharply declines towards negative infinity.
   • Answer: $-\infty$.

3. (c) As $x \to 1^+$, $f(x) \to$

   • Approaching 1 from the right ($x \to 1^+$), $f(x)$ sharply increases towards positive infinity.
   • Answer: $+\infty$.

4. (d) As $x \to \infty$, $f(x) \to$

   • As $x \to \infty$, $f(x)$ appears to approach zero from above, leveling out as it moves to the right.
   • Answer: $0$.

Would you like more details on how to interpret these limits or how to handle similar problems?

Here are some follow-up questions that extend this topic:

1. What do left-hand and right-hand limits mean, and how are they useful?
2. How do asymptotes affect the limits of a function?
3. How do you determine horizontal and vertical asymptotes from a function's equation?
4. What is the significance of infinity in limit calculations?
5. How can you use limits to identify discontinuities in functions?

Tip: When approaching limits involving infinity, observe whether the function levels off (horizontal asymptote) or increases/decreases without bound.