To identify the vertical asymptotes from the graph of the function $f(x)$, we need to locate where the function exhibits behavior approaching infinity (or negative infinity). A vertical asymptote generally occurs where the function is undefined but the behavior of the function approaches $\pm \infty$ on either side of a given x-value.

After analyzing the graph:

• The function appears to have a vertical asymptote near $x = -2$. The function grows rapidly in both directions around this point, indicating an undefined value at $x = -2$.

There are no other obvious vertical asymptotes in the given interval, as the graph does not exhibit this behavior anywhere else.

In summary:

• Vertical asymptote: $x = -2$.

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Related Questions:

1. How do vertical asymptotes relate to the function's domain?
2. What is the behavior of the function as it approaches $x = -2$ from the left and right?
3. Can horizontal asymptotes or oblique asymptotes be identified from this graph?
4. How can we find the exact equation of the function from the graph?
5. What are the conditions under which a function has a vertical asymptote?

Tip:

Vertical asymptotes often arise in rational functions when the denominator equals zero, but the numerator remains non-zero.