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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.

Refer to the graph of the function and complete the statement regarding the behavior of \( f(x) \) as \( x \) approaches different limits.

Explore how to determine the limits of a function as \( x \) approaches infinity or a specific value based on a graph. This problem guides you through understanding horizontal and vertical asymptotes, the concept of approaching positive and negative infinity, and interpreting limit behavior. Suitable for high school students in Grades 10-12.

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