You’ve provided the function \( f(x) = \frac{3x - 5}{6x + 7} \). Here are some key details we can explore:

1. **Domain of the function**: This involves finding the values of \(x\) for which the function is defined.
2. **Intercepts**: Both the x-intercept (where \(f(x) = 0\)) and the y-intercept (where \(x = 0\)).
3. **Asymptotes**: Vertical and horizontal asymptotes based on the behavior of the function as \(x\) approaches certain values.
4. **Critical points**: Points where the derivative \(f'(x)\) equals zero or is undefined, indicating possible maxima, minima, or inflection points.
5. **Behavior as \(x \to \pm\infty\)**: Understanding how the function behaves as \(x\) becomes very large or very small.

Would you like to explore one of these aspects in detail, or do you have any specific questions about the function?

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Here are 5 related questions:
1. How do you find the domain of \(f(x) = \frac{3x - 5}{6x + 7}\)?
2. What are the intercepts of \(f(x)\) and how are they calculated?
3. How do you determine the vertical and horizontal asymptotes of a rational function?
4. How do you find the derivative of \(f(x)\) and identify critical points?
5. What is the end behavior of \(f(x)\) as \(x\) approaches infinity or negative infinity?

**Tip:** For rational functions, vertical asymptotes occur where the denominator is zero, while horizontal asymptotes are determined by comparing the degrees of the numerator and denominator.

Understand the function f(x) = (3x - 5) / (6x + 7) with a detailed analysis of its domain, intercepts, asymptotes, and end behavior. Learn how to find where the function is defined, its intercepts, and how it behaves as x approaches infinity and negative infinity. Suitable for high school students studying advanced algebra and calculus.

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