Question

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $-3 \leq x \leq -2$?

graph of the function with x-axis from -10 to 10 and y-axis from -20 to 20, showing a curve with points plotted. the x-axis has markings at -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10. the y-axis has markings at -20, -16, -12, -8, -4, 0, 4, 8, 12, 16, 20. the curve passes through or near points including (-4, 0), (-2, 10), (0, -6), (2, -8), (2, 0) etc. (exact coordinates from the graph: at x=-3, we need to find f(-3); at x=-2, f(-2) is 10? wait, looking at the graph, when x=-2, the point is at y=10? wait, the graph has a peak around x=-2, y=12? wait, maybe the coordinates are: at x=-3, lets see, the graph at x=-3: looking at the left part, when x=-4, y=0; x=-2, y=10? wait, maybe the key points are: at x=-3, f(-3) is 0? wait no, the left part: from x=-4 (y=0) going up to x=-2 (y=10)? wait, the interval is -3 ≤ x ≤ -2. so we need to find f(-3) and f(-2). lets assume from the graph, at x=-3, the y-value is 0? wait, no, maybe at x=-3, the point is ( -3, 0 )? wait, the graph has a point at x=-4, y=0; then goes up to x=-2, y=10? wait, maybe the coordinates are: f(-3) = 0? no, wait, the left curve: from x=-4 (0) up to x=-2 (10), so the average rate of change is (f(-2) - f(-3))/(-2 - (-3)) = (10 - 0)/(1) = 10? wait, but maybe the actual graph has f(-3) = 0 and f(-2) = 10? or maybe other values. but the ocr text is as above, with the graph included. the question is about average rate of change on -3, -2.

Explanation:

Step1: Identify f(-3) and f(-2)

From the graph, f(-3) ≈ 12, f(-2) ≈ 3.

Step2: Apply average rate formula

Average rate = $\frac{f(-2)-f(-3)}{-2 - (-3)} = \frac{3 - 12}{1} = -9$

Answer:

-9