Question

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

Explanation:

Step1: Recall function properties

A function is negative when its graph is below the \(x -\)axis and decreasing when the slope of the graph is negative (going down - hill from left - to - right).

Step2: Analyze the graph

By observing the graph, we see that the function \(y = f(x)\) is below the \(x -\)axis (negative) and has a negative slope (decreasing) in the intervals \((-\infty,- 2.5)\) and \((1,2)\).

Answer:

\((-\infty,-2.5)\) and \((1,2)\)