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 □ < 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 \( x = -6 \) (left endpoint) to \( x = -1 \) (right endpoint). As \( x \) increases from -6 to -1, the \( y \)-values increase (the line is rising). So the function is increasing on \( -6 < x < -1 \).

Step2: Analyze Segment 2

Segment 2 goes from \( x = -1 \) to \( x = 5 \). As \( x \) increases from -1 to 5, the \( y \)-values decrease (the line is falling). So the function is decreasing on \( -1 < x < 5 \).

Step3: Analyze Segment 3

Segment 3 goes from \( x = 5 \) to \( x = 9 \). As \( x \) increases from 5 to 9, the \( y \)-values increase (the line is rising). So the function is increasing on \( 5 < x < 9 \).

Answer:

The function is increasing on the interval \( -6 < x < -1 \) (segment 1), decreasing on the interval \( -1 < x < 5 \) (segment 2), and increasing on the interval \( 5 < x < 9 \) (segment 3).