1. **Problem Statement:** We are given the graph of a function $f$ defined on the interval $-9 < x < 9$. We need to find all values of $x$ in this open interval where the function has an infinite discontinuity. 2. **Understanding Infinite Discontinuity:** An infinite discontinuity occurs at points where the function approaches infinity or negative infinity, often seen as vertical asymptotes or spikes in the graph. 3. **Analyzing the Graph Description:** The graph shows large positive spikes near $x = -4$ and $x = 1$. These spikes indicate the function values tend to infinity at these points. 4. **Conclusion:** Therefore, the function $f$ has infinite discontinuities at $x = -4$ and $x = 1$ within the interval $-9 < x < 9$. **Final answer:** The values of $x$ where $f$ has infinite discontinuities are $$x = -4 \text{ and } x = 1.$$