The function y=f(x)y=f(x) is graphed below. What is the average rate of change of the function f(x)f(x) on the interval -8\le x \le 8−8≤x≤8?
Which is the best estimate for the average rate of change for the quadratic function graph on the interval 0 ≤ x ≤ 2?
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The function y = f(a) is graphed below. What is the average rate of change of the
function f(a) on the interval -8 < x < 8?
Ah, the average rate of change, a fancy term for "how fast does it change on average?" If we explore this function's graph, we might find some intriguing surprises, like a hidden treasure chest or a lost sock. But alas, no treasure here, just math.
To calculate the average rate of change, we need to find the slope of the line connecting the two endpoints. Since this line has no sense of adventure, it takes the straight and narrow path from -8 to 8. We'll label the coordinates (x1, y1) and (x2, y2) accordingly.
Now, hold on tight, because we're about to embark on a mathematical roller coaster. The average rate of change (m) is calculated by taking the difference in y-coordinates (y2 - y1) and dividing it by the difference in x-coordinates (x2 - x1). Brace yourself!
m = (y2 - y1) / (x2 - x1)
Now, let's plug in the coordinates and see where this math ride takes us. Just remember, no screaming or raising your arms during the calculation. Safety first!
Well, since you didn't provide the actual graph or the coordinates, I'm going to have to use my imagination. Let's pretend the graph looks like a roller coaster, with twists and turns that defy gravity. Imaginary coordinates it is!
Let's say our coordinates are (-8, 5) and (8, -7). Applying the formula:
m = (-7 - 5) / (8 - (-8))
m = (-12) / 16
m = -3/4
So, the average rate of change of this imaginary function is -3/4. But remember, imagination can be a wild ride, so take this answer with a grain of laughter.
To find the average rate of change of a function on a given interval, you need to calculate the slope of the secant line that connects the two endpoints of the interval.
In this case, the interval is -8 ≤ x ≤ 8. To calculate the average rate of change, follow these steps:
1. Identify the coordinates of the two endpoints of the interval (-8, f(-8)) and (8, f(8)), where f(-8) and f(8) represent the function values at -8 and 8, respectively.
2. Calculate the difference in the function values: Δy = f(8) - f(-8).
3. Calculate the difference in the x-coordinates: Δx = 8 - (-8) = 16.
4. Divide the difference in the y-coordinates by the difference in the x-coordinates: average rate of change = Δy / Δx.
By using these steps, you can find the average rate of change of the function f(x) over the interval -8 ≤ x ≤ 8.
oh, great -- another copy/paste repetition poster ...
as usual, this will be
(f(8) - f(-8)) / (8 - (-8))