Question

question
the function f is graphed below. determine the intervals on which f increasing and decreasing.
answer
the function is on the interval <x< (segment 1), on the interval <x< (segment 2),
and on the interval <x< (segment 3).

Explanation:

Step1: Analyze the graph's slope

For a function \(y = f(x)\), if the slope of the graph (the rate of change of \(y\) with respect to \(x\)) is negative, the function is decreasing. If the slope is positive, the function is increasing.

Step2: Identify the intervals

• Segment 1: Looking at the left - most part of the graph (from \(x=-6\) to \(x = - 3\)), as \(x\) increases, \(y\) decreases. So, the function is decreasing on \(-6
• Segment 2: From \(x=-3\) to \(x = 0\), as \(x\) increases, \(y\) increases. So, the function is increasing on \(-3
• Segment 3: From \(x = 0\) to \(x=4\), as \(x\) increases, \(y\) increases. So, the function is increasing on \(0

Answer:

The function is decreasing on the interval $-6 < x < -3$ (segment 1), increasing on the interval $-3 < x < 0$ (segment 2), and increasing on the interval $0 < x < 4$ (segment 3).