Question

determine the intervals on which the function is (a) increasing; (b) decreasing; (c) constant. (a) the function is increasing on the interval(s) (-4, 1). (use a comma to separate answers as needed. type your answer in interval notation.)

Explanation:

Step1: Understand increasing - function concept

A function is increasing when as \(x\) increases, \(y\) also increases. Looking at the graph, we see the \(y\) - values rise as \(x\) goes from - 4 to 1.

Step2: Determine decreasing intervals

A function is decreasing when as \(x\) increases, \(y\) decreases. From the graph, the function is decreasing on the interval \((3,5)\).

Step3: Determine constant intervals

A function is constant when \(y\) does not change as \(x\) changes. The function is constant on the interval \((1,3)\).

Answer:

(a) \((-4,1)\)
(b) \((3,5)\)
(c) \((1,3)\)