Final answer:
The limit of f(x) as x approaches 3 cannot be precisely determined without the specific equation for f(x). However, if f(x) is continuous, the limit would be the function's value at x = 3. For the given options, y = x² seems to fit the behavior of the function near x = 3, given its increasing value and decreasing positive slope.
Step-by-step explanation:
The question is asking to find the limit of the function f(x) as x approaches 3. To find this limit, we can look at the characteristics of the function around x = 3. Based on the provided information, at x = 3, the function f(x) has a positive value and a positive slope. Since the slope is positive and decreasing in magnitude, we can conclude that the function is increasing but at a decreasing rate as x approaches 3.
However, the question does not provide the specific form of the function f(x), so we cannot calculate the exact limit without more information. If f(x) were continuous at x = 3, then the limit of f(x) as x approaches 3 would simply be the value of f(x) at x = 3. Given the choices provided (y = 13x or y = x²) and the conditions described, y = x² seems to be the more likely representation of f(x) near x = 3, as it shows an increasing value with a positive and decreasing slope.