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In this question, you're asked how the limit of a polynomial function \( p(x) \) is calculated as \( x \) approaches \( a \).

### Understanding the Concept:
If \( p(x) \) is a polynomial function, limits behave very nicely. Polynomial functions are continuous, meaning that their limit as \( x \) approaches any value \( a \) is simply the value of the polynomial at \( a \). This is because polynomials have no breaks, jumps, or holes in their graphs.

### Conclusion:
For a polynomial \( p(x) \), 
\[
\lim_{x \to a} p(x) = p(a)
\]
Thus, the correct answer is **C.** \( \lim_{x \to a} p(x) = p(a) \).

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Would you like further details or explanations?

Here are 5 related questions for deeper understanding:
1. What are the general properties of continuous functions?
2. How do limits behave for rational functions compared to polynomial functions?
3. Why are polynomial functions considered continuous everywhere?
4. What happens if the limit approaches a point where the polynomial is undefined (like division by zero)?
5. Can limits of non-polynomial functions be calculated in the same way?

**Tip:** Always check if the function you're dealing with is continuous at the point you're evaluating. Continuous functions make calculating limits straightforward!

How is \( \lim_{x \to a} p(x) \) calculated if \( p \) is a polynomial function?

Learn how to calculate the limit of a polynomial function as x approaches a specific value. Understand the continuity of polynomials and how limits behave for such functions, suitable for Grades 11-12 students.

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