using the graph of the function $y = f(x)$, answer the following questions.\na) on what intervals is $f$…

using the graph of the function $y = f(x)$, answer the following questions.\na) on what intervals is $f$ increasing? enter your answer in interval notation.\ninterval(s)\nb) on what intervals is $f$ decreasing? enter your answer in interval notation.\ninterval(s)

using the graph of the function $y = f(x)$, answer the following questions.\na) on what intervals is $f$ increasing? enter your answer in interval notation.\ninterval(s)\nb) on what intervals is $f$ decreasing? enter your answer in interval notation.\ninterval(s)

Answer

Explanation:

Step1: Recall increasing - function property

A function $y = f(x)$ is increasing when, as $x$ increases, $y$ also increases. Visually, the graph goes up from left - to - right.

Step2: Identify increasing intervals from the graph

From the graph, we can see that the function is increasing on the intervals $(-5,-2)$ and $(1,5)$.

Step3: Recall decreasing - function property

A function $y = f(x)$ is decreasing when, as $x$ increases, $y$ decreases. Visually, the graph goes down from left - to - right.

Step4: Identify decreasing intervals from the graph

From the graph, the function is decreasing on the intervals $(-2,1)$.

Answer:

a) $(-5,-2)\cup(1,5)$ b) $(-2,1)$