Question

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $-4 \leq x \leq -3$? (image of the graph is shown with x-axis from -10 to 10 and y-axis from -100 to 100, with plotted points and a curve.)

Explanation:

Step1: Find f(-4) and f(-3)

From the graph, when \( x = -4 \), \( f(-4) = 0 \) (since the graph crosses the x - axis at \( x=-4 \)). When \( x=-3 \), we look at the y - value of the point on the graph at \( x = - 3 \). From the grid, we can see that the y - value at \( x=-3 \) is 40 (since it's on the vertical line corresponding to \( y = 40 \) and horizontal line \( x=-3 \)).

Step2: Apply the 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, \( a=-4 \), \( b = - 3 \), \( f(a)=f(-4)=0 \), and \( f(b)=f(-3)=40 \).

Substitute these values into the formula: \( \frac{f(-3)-f(-4)}{-3-(-4)}=\frac{40 - 0}{-3 + 4}=\frac{40}{1}=40 \).

Answer:

40