Final answer:
After simplifying the original function, (x² - 9)/(x - 3) becomes x + 3. Substituting x = -3 into this simplified function gives us a limit of 0. option d is the correct answer.
Step-by-step explanation:
The question asks us to find the limit of the function f(x) = (x² - 9)/(x - 3) as x approaches -3. To solve this limit, we first simplify the expression by factoring the numerator which is a difference of squares; x² - 9 can be written as (x + 3)(x - 3). The term (x - 3) in the numerator and denominator cancel each other out, as long as x is not equal to 3 to avoid division by zero.
Therefore, we are left with the function f(x) = x + 3, and we need to find the limit as x approaches -3.
Substituting -3 into the simplified function, we get f(-3) = (-3) + 3 = 0. Therefore, the limit exists and the correct answer is option d) 0.
There's no need to apply complex limit strategies since the function simplifies to a linear one, which is continuous and differentiable everywhere.