can you give me a problem of a function graphing so that i can practice it graphing my own

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.

Practice graphing the rational function f(x) = (2x^2 - 3x + 1) / (x^2 - 4) by identifying key features like intercepts, vertical and horizontal asymptotes, and analyzing its behavior as x approaches infinity. This problem is suitable for students in Grades 10-12.

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