Question

the function f is graphed below. determine the intervals on which f increasing and decreasing.

Explanation:

Step1: Identify increasing intervals

A function increases when as $x$ increases, $y$ increases. Look at Segment 1: $x$ from $-5$ to $-2$, $y$ rises from $-6$ to $5$. Segment 2: $x$ from $-2$ to $3$, $y$ rises from $5$ to $7$.

Step2: Identify decreasing interval

A function decreases when as $x$ increases, $y$ decreases. Look at Segment 3: $x$ from $3$ to $9$, $y$ falls from $7$ to $3$.

Answer:

Increasing on $(-5, -2)$ and $(-2, 3)$
Decreasing on $(3, 9)$