numpy as np import matplotlib.pyplot as plt

Define the function

def F(x): return (x**2 + 4*x - 12) / (x - 2)

Define the x values, avoiding x = 2 (where the denominator is 0)

x = np.linspace(-10, 10, 1000) x = x[x != 2]

Plot the function

plt.figure(figsize=(8, 6)) plt.plot(x, F(x), label="F(x) = (x^2 + 4x - 12) / (x - 2)", color='blue') plt.axvline(x=2, color='red', linestyle='--', label="Vertical Asymptote at x=2") plt.axhline(y=0, color='black', linewidth=0.8)

Set labels and title

plt.title("Graph of F(x) = (x^2 + 4x - 12) / (x - 2)") plt.xlabel("x") plt.ylabel("F(x)") plt.legend() plt.grid()

Show the plot

plt.show()Here's the graph of the function $F(x) = \frac{x^2 + 4x - 12}{x - 2}$. The graph includes:

• A vertical asymptote at $x = 2$, where the denominator becomes zero.
• The curve defined by the rational function $F(x)$ across other values of $x$.

Would you like to explore further details about this function, such as its critical points, asymptotes, or intercepts?

Here are 5 related questions you might consider:

1. What are the x- and y-intercepts of this function?
2. How does the vertical asymptote at $x = 2$ affect the behavior of the graph?
3. Can we find the horizontal asymptote, if it exists, for this function?
4. How does the graph behave as $x \to \pm \infty$?
5. What is the domain and range of this function?

Tip: Understanding the asymptotes and critical points can help you analyze the behavior of any rational function.