Question

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

A function $y = f(x)$ is increasing on an interval if for any two points $x_1$ and $x_2$ in the interval with $x_1f(x_2)$ for $x_1 < x_2$.

Step2: Analyze the graph

Looking at the graph of $y = f(x)$, as we move from left - to - right, the function is increasing when the graph is going up. We can see that the function $y = f(x)$ is increasing on the interval $(-\infty,2)$.

Step3: Analyze the decreasing part

The function is decreasing when the graph is going down. The function $y = f(x)$ is decreasing on the interval $(2,\infty)$.

Answer:

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