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Given the function \( f(x) = \frac{6x^2 - 9x + 4}{2x - 3} \), compute the following limits:

1. \( \lim_{{x \to 2}} f(x) \)
   \[ \text{Result: } \boxed{4} \]

2. \( \lim_{{x \to 0}} f(x) \)
   \[ \text{Result: } \boxed{2} \]

3. \( \lim_{{x \to 1}} f(x) \)
   \[ \text{Result: } \boxed{5} \]

4. \( \lim_{{x \to -\infty}} f(x) \)
   \[ \text{Result: } \boxed{3} \]

5. \( \lim_{{x \to \infty}} f(x) \)
   \[ \text{Result: } \boxed{3} \]

If these are the answers given in the image, I can help confirm them by solving the limits. Would you like a detailed explanation of each step?

Given the function f(x) = (6x^2 - 9x + 4) / (2x - 3), compute the following limits:
1. lim(x → 2) f(x)
2. lim(x → 0) f(x)
3. lim(x → 1) f(x)
4. lim(x → -∞) f(x)
5. lim(x → ∞) f(x)

Explore the step-by-step process of calculating limits for the function f(x) = (6x^2 - 9x + 4) / (2x - 3) as x approaches specific values. This problem involves key calculus concepts such as limits, rational functions, and the application of limit laws. Suitable for students in Grades 11-12.

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