Question

select all the intervals where f is decreasing. y = f(x) choose all answers that apply: a -4.5 < x < -4 b -0.5 < x < 0 c 1 < x < 2 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 has a negative - slope on the interval.

Step2: Analyze each option

• Option A: In the interval $-4.5 < x<-4$, the function is increasing as we move from left - to - right (the $y$ - values are getting larger).
• Option B: In the interval $-0.5 < x < 0$, the function is increasing as we move from left - to - right (the $y$ - values are getting larger).
• Option C: In the interval $1 < x < 2$, the function is decreasing as we move from left - to - right (the $y$ - values are getting smaller).

Answer:

C. $1 < x < 2$