Question

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

Explanation:

Step1: Recall the definition of increasing and decreasing functions

A function \(y = f(x)\) is increasing on an interval if, for any two points \(x_1\) and \(x_2\) in the interval with \(x_1

Step2: Analyze the graph

Looking at the graph:

• For segment 1: As \(x\) increases (from left - to - right), \(y\) increases. The left - most \(x\) value of this segment is \(x=- 6\) and the right - most \(x\) value (where the function changes its behavior) is \(x=-1\).
• For segment 2: As \(x\) increases (from left - to - right), \(y\) decreases. The left - most \(x\) value of this segment is \(x = - 1\) and the right - most \(x\) value (where the function changes its behavior) is \(x = 2\).
• For segment 3: As \(x\) increases (from left - to - right), \(y\) decreases. The left - most \(x\) value of this segment is \(x=2\) and the right - most \(x\) value is \(x = 7\).

Answer:

The function is increasing on the interval \(-6