Final answer:
The end behavior of the function f(x) = -(1/3)x + 3 is that it decreases as x approaches infinity and increases as x approaches negative infinity. Neither of the given options, y = 13x or y = x², correctly describes a function with a positive slope that decreases in magnitude as x increases.
Step-by-step explanation:
The question concerns the end behavior of the linear function f(x) = -\(\frac{1}{3}\)x + 3. The end behavior of a function describes how the function behaves as x approaches positive or negative infinity. For the given linear function, as x goes to positive infinity (x → ∞), the function decreases because the slope is negative, and as x goes to negative infinity (x → -∞), the function increases.
Now let us address the student's confusion regarding the function at x = 3. The choices given were a. y = 13x and b. y = x². The key detail here is that the slope is positive but decreasing in magnitude as x increases. This characteristic is not consistent with option a, as it suggests a constant positive slope with no decrease. Option b, while having a positive slope that increases with x, does not exhibit a decreasing magnitude. Thus, neither option accurately describes the behavior of the function at x = 3 as given in the question.