Question

the function $y = f(x)$ is graphed below. plot a line segment connecting the points on $f$ where $x = -1$ and $x = 1$. use the line segment to determine the average rate of change of the function $f(x)$ on the interval $-1 \leq x \leq 1$.

plot a line segment by clicking in two locations. click a segment to delete it.

Explanation:

Step1: Find f(-1) and f(1)

From the graph, when \( x = -1 \), we look at the y - value of the point on the function. By observing the graph, \( f(-1)=-10 \). When \( x = 1 \), the y - value of the point on the function is \( f(1)=-25 \).

Step2: Apply average rate of change formula

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, \( a=-1 \), \( b = 1 \), \( f(a)=f(-1)=-10 \), \( f(b)=f(1)=-25 \).

Substitute these values into the formula: \( \frac{f(1)-f(-1)}{1-(-1)}=\frac{-25-(-10)}{1 + 1}=\frac{-25 + 10}{2}=\frac{-15}{2}=-7.5 \)

Answer:

The average rate of change is \(-\frac{15}{2}\) (or - 7.5)