Sure! Here's a problem you can try for graphing a function:

Problem: Graph the following function and identify key features such as intercepts, asymptotes (if any), and behavior as $x \to \infty$ and $x \to -\infty$.

$f(x) = \frac{2x^2 - 3x + 1}{x^2 - 4}$

Instructions:

1. Determine the domain of the function.
2. Identify vertical asymptotes by finding the values of $x$ that make the denominator zero.
3. Find the horizontal asymptote by analyzing the degrees of the numerator and denominator.
4. Calculate the $x$- and $y$-intercepts.
5. Sketch the graph of the function based on the above findings.

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Would you like more details on how to approach solving this problem?

Related Questions:

1. What are vertical asymptotes, and how do you find them?
2. How can you determine if a function has a horizontal or slant asymptote?
3. What are the steps to find the intercepts of a rational function?
4. How does the degree of the numerator and denominator influence the graph of a rational function?
5. What happens to the function as $x \to \infty$ or $x \to -\infty$?

Tip: When graphing rational functions, always factor both the numerator and denominator if possible—it simplifies the identification of key features like intercepts and asymptotes.