Question

a. $f(x)$ is increasing and positive on the interval $(-infty, 3)$.

b. $f(x)$ is decreasing and positive on the interval $(-infty, 3)$.

c. $f(x)$ is increasing and negative on the interval $(-infty, 3)$.

d. $f(x)$ is decreasing and negative on the interval $(-infty, 3)$

Explanation:

To determine the correct option, we analyze the graph's behavior:

1. Increasing/Decreasing: The graph (the red curve) has a negative slope (from left to right, it is going down), so the function is decreasing on its domain (which includes \((-\infty, 3)\) as per the context).
2. Positive/Negative: The graph is above the x - axis (since the red curve is in the region where \(y>0\)) on the interval \((-\infty, 3)\), so the function is positive there.

Option A is wrong because the function is not increasing. Option C is wrong as the function is not increasing and not negative. Option D is wrong as the function is not negative. Option B matches the analysis (decreasing and positive on \((-\infty, 3)\)).

Answer:

B. \( f(x) \) is decreasing and positive on the interval \((-\infty, 3)\).