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 □ < x < □ (segment 1), ▼ on the interval □ < x < □ (segment 2), and ▼ on the interval □ < x < □ (segment 3).

Explanation:

Step1: Analyze Segment 1

Segment 1 goes from \( x = -6 \) to \( x = -2 \). As \( x \) increases, \( y \) decreases (since the line is going down from left to right). So the function is decreasing here. The interval is \( -6 < x < -2 \).

Step2: Analyze Segment 2

Segment 2 goes from \( x = -2 \) to \( x = 3 \). As \( x \) increases, \( y \) increases (the line is going up from left to right). So the function is increasing here. The interval is \( -2 < x < 3 \).

Step3: Analyze Segment 3

Segment 3 goes from \( x = 3 \) to \( x = 7 \). As \( x \) increases, \( y \) increases (the line is going up from left to right). So the function is increasing here. The interval is \( 3 < x < 7 \).

Answer:

The function is decreasing on the interval \( -6 < x < -2 \) (segment 1), increasing on the interval \( -2 < x < 3 \) (segment 2), and increasing on the interval \( 3 < x < 7 \) (segment 3).