Question

practice assignment 3.3 rates of change a
the function graphed above is:
increasing on the interval(s)
decreasing on the interval(s)

Explanation:

Step1: Recall increasing - decreasing function definition

A function $y = f(x)$ is increasing when the slope of the tangent line is positive and decreasing when the slope of the tangent line is negative.

Step2: Analyze the graph

Looking at the graph, we see that the function is increasing when moving from left - to - right and the $y$ - values are getting larger. The function is increasing on the interval $(-4,-1)$.

Step3: Analyze the decreasing part

The function is decreasing when moving from left - to - right and the $y$ - values are getting smaller. The function is decreasing on the intervals $(-\infty,-4)\cup(-1,\infty)$.

Answer:

Increasing on the interval(s): $(-4,-1)$
Decreasing on the interval(s): $(-\infty,-4)\cup(-1,\infty)$