Question

the function ( f ) is graphed below. determine the intervals on which ( f ) is 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: Analyze Segment 1 (Increasing)

Segment 1 is a line from \( x = -3 \) (left end) to \( x = -1 \) (right end), and as \( x \) increases, \( y \) increases. So the interval for increasing here is \( -3 < x < -1 \).

Step2: Analyze Segment 2 (Decreasing)

Segment 2 is a line from \( x = -1 \) to \( x = 2 \), and as \( x \) increases, \( y \) decreases. So the interval for decreasing here is \( -1 < x < 2 \).

Step3: Analyze Segment 3 (Decreasing)

Segment 3 is a line from \( x = 2 \) to \( x = 7 \), and as \( x \) increases, \( y \) decreases (slightly, but still decreasing). So the interval for decreasing here is \( 2 < x < 7 \).

Answer:

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