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The graph provided depicts a function \( g(x) \) with a vertical asymptote at \( x = -2 \) (indicated by the red line). The curve suggests the following behaviors as \( x \) approaches different values:

1. **As \( x \) approaches negative infinity (\( x \to -\infty \)):**
   - The function appears to decrease without bound, suggesting \( g(x) \) tends towards negative infinity as \( x \to -\infty \).
   - Thus, \( \lim_{x \to -\infty} g(x) = -\infty \).

2. **As \( x \) approaches positive infinity (\( x \to +\infty \)):**
   - The function continues to rise without bound, indicating that \( g(x) \) approaches positive infinity.
   - Thus, \( \lim_{x \to +\infty} g(x) = +\infty \).

3. **As \( x \) approaches -2 from the right (\( x \to -2^+ \)):**
   - The function rises sharply, indicating that \( g(x) \) approaches positive infinity.
   - This is consistent with the provided answer, \( \lim_{x \to -2^+} g(x) = +\infty \).

4. **As \( x \) approaches -2 from the left (\( x \to -2^- \)):**
   - The function falls rapidly, indicating that \( g(x) \) approaches negative infinity.
   - Therefore, \( \lim_{x \to -2^-} g(x) = -\infty \).

### Filling in the Blanks:

1. \( \lim_{x \to -\infty} g(f(x)) = -\infty \)
2. \( \lim_{x \to +\infty} g(f(x)) = +\infty \)
3. \( \lim_{x \to 1^+} g(f(x)) = +\infty \) (This is already correct.)
4. \( \lim_{x \to 0} g(f(x)) \): Since \( x \) is not close to the asymptote \( x = -2 \), we would need more context or information about \( f(x) \) or the specific behavior of \( g(x) \) near \( x = 0 \). This limit might involve further information about the function \( f(x) \) to make an accurate determination.

Would you like to explore more details on this or have any specific questions?

### Relative Questions:
1. How do vertical asymptotes affect the limits of functions?
2. What happens to the limit of a function when approaching infinity?
3. How can you determine the end behavior of a function from its graph?
4. How do you find the limit of a composite function like \( g(f(x)) \)?
5. What methods can be used to find limits involving infinity?

**Tip:** Always check the behavior of a function near its asymptotes to correctly determine the limits as the function approaches these critical points.

The graph below depicts a function g(x). Its one asymptote is indicated in red. Various limits for g(f(x)) are requested, with one value already provided: lim (x → 1^+) g(f(x)) = ∞.

Explore how to determine the limits of the function g(x) as it approaches infinity, negative infinity, and near its vertical asymptote at x = -2. This problem involves advanced calculus concepts like limits and function behavior near asymptotes, suitable for students in Grades 11-12 or college-level calculus.

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