Question

1. where is f(x) both positive and decreasing? (-∞,-3) only (-∞,-2.5) only (-2.5,1) only (-∞,-3) and (1,2)

Explanation:

Step1: Recall function behavior rules

A function $y = f(x)$ is positive when $f(x)>0$ (above the x - axis) and decreasing when its slope is negative.

Step2: Analyze the graph for positive regions

The graph of $y = f(x)$ is above the x - axis (positive) in certain intervals. By observing, we see it's positive in parts of the domain.

Step3: Analyze the graph for decreasing regions

The graph is decreasing when the curve goes down - hill as we move from left to right.

Step4: Find the overlapping intervals

By carefully observing the graph, we find that the function is both positive and decreasing in the interval $(-2.5,1)$.

Answer:

(-2.5, 1) only