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 is from \( x = -8 \) to \( x = -5 \) (looking at the left - most segment). As \( x \) increases from - 8 to - 5, the \( y \) - value of the function increases. So the function is increasing on the interval \( -8 < x < -5 \).

Step2: Analyze Segment 2

Segment 2 is from \( x=-5\) to \( x = 0\) (the middle - left segment). As \( x \) increases from - 5 to 0, the \( y \) - value of the function decreases. So the function is decreasing on the interval \( -5 < x < 0 \).

Step3: Analyze Segment 3

Segment 3 is from \( x = 0\) to \( x = 4\) (the right - most segment). As \( x \) increases from 0 to 4, the \( y \) - value of the function decreases. So the function is decreasing on the interval \( 0 < x < 4 \).

Answer:

The function is \(\boldsymbol{\text{increasing}}\) on the interval \(\boldsymbol{-8}