Final answer:
The limit of the function 3x² + 5x + 3 as x approaches -3 is evaluated by direct substitution, yielding a result of 15. The given options do not include this correct answer, suggesting an error in the provided options.
Step-by-step explanation:
The question asks to evaluate the limit as x approaches -3 for the polynomial function 3x² + 5x + 3. To find this limit, we simply substitute the value of -3 into the function, because polynomials are continuous everywhere, and particularly at the point x = -3.
So we calculate:
3(-3)² + 5(-3) + 3
= 3(9) - 15 + 3
= 27 - 15 + 3
= 15
Therefore, the limit of the function as x approaches -3 is 15, which is not one of the options provided in the original question, indicating a possible typo in the question.