Here's the graph of $f(x) = \sin\left(\frac{1}{x}\right)$. As expected, the function oscillates rapidly between -1 and 1 as $x$ approaches 0 from both sides, and the oscillations become more gradual as $|x|$ increases. The graph doesn't include $x = 0$ because the function is undefined there.

Key Observations:

• For $x$ close to 0, the graph oscillates infinitely, which is why it appears densely packed near the origin.
• For larger values of $x$, the oscillations smooth out and resemble a standard sine curve but with decreasing frequency.

Would you like more details or have any questions? Here are some related questions to consider:

1. What happens if we try to evaluate the limit of $\sin\left(\frac{1}{x}\right)$ as $x$ approaches 0?
2. How does the behavior of $f(x) = \sin\left(\frac{1}{x}\right)$ change when you introduce a shift or scaling factor?
3. Can you describe why the function is not continuous at $x = 0$?
4. What other functions behave similarly near $x = 0$?
5. How would the graph change if we used $\cos\left(\frac{1}{x}\right)$ instead of $\sin\left(\frac{1}{x}\right)$?

Tip: Functions with oscillations near a point, like $\sin\left(\frac{1}{x}\right)$, often have undefined limits at that point due to the rapid change in values.