Question

using the graph of the function y = f(x), answer the following questions.

a) what interval(s) is f increasing? enter your answer in interval notation.

b) on what interval(s) is f decreasing? enter your answer in interval notation.

Explanation:

Step1: Recall increasing - decreasing concept

A function $y = f(x)$ is increasing when the graph goes up as we move from left - to - right and decreasing when the graph goes down as we move from left - to - right.

Step2: Identify increasing interval

Looking at the graph, the function $y = f(x)$ is going up (increasing) for $x$ values starting from $x = 2$ and going to the right. In interval notation, the increasing interval is $(2,\infty)$.

Step3: Identify decreasing interval

The function $y = f(x)$ is going down (decreasing) for $x$ values starting from negative infinity and going up to $x = 2$. In interval notation, the decreasing interval is $(-\infty,2)$.

Answer:

a) $(2,\infty)$
b) $(-\infty,2)$