you are told that the average rate of change of a particular function is always negative. what can you…

Answer:

The graph of the function is always decreasing.

Explanation:

Step1: Recall rate - of - change concept

The average rate of change of a function $y = f(x)$ over an interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$.

Step2: Analyze negative rate of change

If $\frac{f(b)-f(a)}{b - a}<0$, and $b>a$ (since $b - a>0$ for a non - degenerate interval), then $f(b)-f(a)<0$, which means $f(b)<f(a)$. So as $x$ increases (from $a$ to $b$), the value of the function $y = f(x)$ decreases. This implies that the graph of the function is always decreasing.