Question

select all the intervals where f is decreasing. y = f(x) choose all answers that apply: a -2 < x < -1.5 b -1 < x < 0 c 0 < x < 1 d none of the above

Explanation:

Step1: Recall decreasing - function property

A function $y = f(x)$ is decreasing on an interval if for any two points $x_1$ and $x_2$ in the interval with $x_1f(x_2)$. Graphically, the function is decreasing when the graph goes down - hill as we move from left to right.

Step2: Analyze the given graph

Looking at the graph of $y = f(x)$, we observe the behavior of the function on the given intervals:

• For the interval $-2 < x<-1.5$, the function is increasing (the graph is going uphill as we move from left - to - right).
• For the interval $-1 < x<0$, the function is increasing (the graph is going uphill as we move from left - to - right).
• For the interval $0 < x<1$, the function is decreasing (the graph is going downhill as we move from left - to - right).

Answer:

C. $0 < x<1$