The question asks to state all values of $x$ in the open interval $-9 < x < 9$ for which the function $f(x)$ has an infinite discontinuity.

Looking at the graph of $f(x)$, an infinite discontinuity occurs when the function approaches infinity or negative infinity on either side of a point, which typically corresponds to a vertical asymptote.

From the graph:

• The function has an infinite discontinuity at $x = -6$, as the graph shows a vertical asymptote at this point.
• Similarly, there is an infinite discontinuity at $x = 3$, where another vertical asymptote exists.

Thus, the values of $x$ for which the function has infinite discontinuities in the interval $-9 < x < 9$ are: $x = -6, 3$

Would you like further details or have any other questions?

Here are some related questions for practice:

1. What is the difference between a removable and an infinite discontinuity?
2. How would you identify a jump discontinuity on a graph?
3. Why do vertical asymptotes lead to infinite discontinuities?
4. How can you tell from a function's equation where infinite discontinuities might occur?
5. What is the significance of asymptotes in determining the behavior of a function?

Tip: When analyzing graphs for discontinuities, always check if the function approaches infinity near certain values of $x$, as this typically indicates an infinite discontinuity.