which graph has an average rate of change of approximately -1 over the interval -2,6?

Answer

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is given by $\frac{f(b)-f(a)}{b - a}$. Here, $a=-2$, $b = 6$, so the average rate of change is $\frac{f(6)-f(-2)}{6-(-2)}=\frac{f(6)-f(-2)}{8}$. We want this value to be approximately $- 1$, so $f(6)-f(-2)\approx - 8$.

Step2: Analyze each graph

For each graph, find the $y$ - values at $x=-2$ and $x = 6$.

For the first graph: Estimate the $y$ - value at $x=-2$ and $x = 6$. Let's assume $y_1$ at $x=-2$ and $y_2$ at $x = 6$. Calculate $y_2 - y_1$.
For the second graph: Do the same. Estimate the $y$ - values at $x=-2$ and $x = 6$.
For the third graph: Estimate the $y$ - values at $x=-2$ and $x = 6$.
For the fourth graph: Estimate the $y$ - value at $x=-2$ (say $y_{-2}$) and at $x = 6$ (say $y_6$). If we assume the $y$ - value at $x=-2$ is around $7$ and the $y$ - value at $x = 6$ is around $-1$, then $y_6-y_{-2}=-1 - 7=-8$. The average rate of change $\frac{y_6 - y_{-2}}{6-(-2)}=\frac{-8}{8}=-1$.

Answer:

The fourth graph.