1. We are asked to find the limits of polynomial, rational, and radical functions. 2. The limit of a polynomial function as $x$ approaches a value $a$ is simply the value of the polynomial at $a$, because polynomials are continuous everywhere. 3. For rational functions, which are ratios of polynomials, the limit as $x$ approaches $a$ depends on whether the denominator is zero at $a$. If the denominator is not zero, the limit is the ratio of the polynomials evaluated at $a$. If the denominator is zero, we may need to simplify or use other limit techniques. 4. For radical functions, limits can be found by direct substitution if the expression under the root is continuous and non-negative near $a$. Otherwise, rationalizing or other algebraic manipulations may be needed. 5. Example: Find $\lim_{x \to 2} \frac{x^2 - 4}{x - 2}$. 6. Direct substitution gives $\frac{2^2 - 4}{2 - 2} = \frac{0}{0}$, an indeterminate form. 7. Factor numerator: $x^2 - 4 = (x - 2)(x + 2)$. 8. Simplify the expression: $$\frac{\cancel{(x - 2)}(x + 2)}{\cancel{(x - 2)}} = x + 2$$ 9. Now substitute $x = 2$: $$2 + 2 = 4$$ 10. Therefore, $\lim_{x \to 2} \frac{x^2 - 4}{x - 2} = 4$. This method applies similarly to other polynomial, rational, and radical limits.