y = (x ^ 2 - x + 1)/(x ^ 2 + x + 1) draw the graph 

Here is the graph of the function \( y = \frac{x^2 - x + 1}{x^2 + x + 1} \). The function is symmetric and has no asymptotes. The curve smoothly transitions, and as \( x \) becomes very large in either direction, the function approaches a horizontal asymptote at \( y = 1 \).

Would you like further details on the graph or have any questions? 

Here are 8 related questions:
1. How do you determine the horizontal asymptote of a rational function?
2. What are the critical points of this function?
3. Can this function have any vertical asymptotes?
4. What does the symmetry of the function imply?
5. How do you find the maximum and minimum values of the function?
6. What is the domain and range of this function?
7. How does the function behave near \( x = 0 \)?
8. How can this function be used in a real-world scenario?

**Tip:** When analyzing rational functions, checking the behavior as \( x \) approaches infinity can help identify horizontal asymptotes.

Explore the graph of the rational function y = (x^2 - x + 1) / (x^2 + x + 1), which exhibits symmetric behavior and approaches a horizontal asymptote at y = 1. Understand the function's domain, range, and asymptotic properties. Suitable for advanced high school students.

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