import numpy as np import matplotlib.pyplot as plt

Define the function y = tan(2x)

x = np.linspace(-np.pi, np.pi, 1000) y = np.tan(2 * x)

Avoid plotting values near the vertical asymptotes of the tangent function

y[np.abs(y) > 10] = np.nan

Create the plot

plt.figure(figsize=(8, 6)) plt.plot(x, y, label=r"$y = \tan(2x)$") plt.axhline(0, color='black', linewidth=0.5, linestyle='--') plt.axvline(0, color='black', linewidth=0.5, linestyle='--') plt.title("Graph of $y = \tan(2x)$") plt.xlabel("$x$") plt.ylabel("$y$") plt.ylim(-10, 10) plt.grid(True, linestyle='--', alpha=0.7) plt.legend() plt.show() <<ImageDisplayed>>successHere is the graph of $y = \tan(2x)$. The graph demonstrates the periodic behavior of the tangent function with the argument $2x$, doubling its frequency compared to $y = \tan(x)$. It also shows vertical asymptotes at $x = \pm \frac{\pi}{4}, \pm \frac{3\pi}{4}, \dots$, where the function is undefined.

Would you like more details or have any specific questions about this graph?

Related Questions:

1. What is the period of the function $y = \tan(2x)$?
2. How does the graph of $y = \tan(2x)$ compare to $y = \tan(x)$?
3. What are the vertical asymptotes of $y = \tan(2x)$?
4. How can transformations like $y = \tan(2x) + c$ affect the graph?
5. How would the graph change if $y = \tan(kx)$ for a general $k$?

Tip:

Remember that the period of $\tan(kx)$ is $\frac{\pi}{k}$, and its vertical asymptotes occur where $kx = \frac{\pi}{2} + n\pi$.