Question

the function $y = f(x)$ is graphed below. plot a line segment connecting the points on $f$ where $x = -6$ and $x = -1$. use the line segment to determine the average rate of change of the function $f(x)$ on the interval $-6 leq x leq -1$.
plot a line segment by clicking in two locations. click a segment to delete it.

Explanation:

Step1: Identify the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) on the interval \([a,b]\) is \(\frac{f(b)-f(a)}{b - a}\). Here, \(a=-6\) and \(b = - 1\).

Step2: Find the values of \(f(-6)\) and \(f(-1)\)

From the graph, when \(x=-6\), \(y=f(-6)=-80\) (assuming the point \((-6,-80)\) based on the grid - like structure of the graph). When \(x = - 1\), \(y=f(-1)=50\) (assuming the point \((-1,50)\) based on the graph's appearance).

Step3: Substitute into the formula

Substitute \(a=-6\), \(b=-1\), \(f(a)=-80\), and \(f(b) = 50\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{50-(-80)}{-1-(-6)}=\frac{50 + 80}{-1 + 6}=\frac{130}{5}\).

Answer:

\(26\)