If you’re trying to find the average rate of change from a graph there are a few things you’ll need to keep in mind. First you’ll need to identify the two points on the graph that you want to find the average rate of change between. Then you’ll need to calculate the change in y (Δy) between those two points. Once you have Δy you’ll need to calculate the change in x (Δx) between those same two points. Finally you’ll divide Δy by Δx to find the average rate of change.
To start let’s take a look at an example graph:
In this graph we can see that the y-axis is labeled “Height” and the x-axis is labeled “Time.” We can also see that there are two points labeled on the graph “A” and “B.” We want to find the average rate of change between points A and B.
To do this we need to first calculate Δy. We can see that at point A the height is 5 units. At point B the height is 10 units. This means that Δy is 5 units. Now we need to calculate Δx. We can see that at point A the time is 0 seconds. At point B the time is 10 seconds. This means that Δx is 10 seconds.
Now that we have Δy and Δx we can calculate the average rate of change. To do this we simply divide Δy by Δx. In our example this would be 5 units divided by 10 seconds which equals 0.5 units per second. This is the average rate of change between points A and B.
Now that you know how to find the average rate of change from a graph you can use this technique to answer all sorts of questions. For example you could use it to find the average rate of change of a car’s speed over time or the average rate of change of a person’s weight over time. The possibilities are endless!
What is the average rate of change of the function f(x) = x^2 from x = 1 to x = 3?
The average rate of change of the function f(x) = x^2 from x = 1 to x = 3 is 4.
What is the average rate of change of the function f(x) = x^2 from x = 0 to x = 4?
The average rate of change of the function f(x) = x^2 from x = 0 to x = 4 is 8.
What is the average rate of change of the function f(x) = 2x from x = 1 to x = 5?
The average rate of change of the function f(x) = 2x from x = 1 to x = 5 is 10.
What is the average rate of change of the function f(x) = 1/x from x = 1 to x = 5?
The average rate of change of the function f(x) = 1/x from x = 1 to x = 5 is -0.
8.
What is the average rate of change of the function f(x) = 1/x from x = 2 to x = 6?
The average rate of change of the function f(x) = 1/x from x = 2 to x = 6 is -0.
6.
What is the average rate of change of the function f(x) = 1/x from x = 1 to x = 6?
The average rate of change of the function f(x) = 1/x from x = 1 to x = 6 is -0.
5.
What is the average rate of change of the function f(x) = 1/x from x = 3 to x = 9?
The average rate of change of the function f(x) = 1/x from x = 3 to x = 9 is -0.
4.
What is the average rate of change of the function f(x) = 1/x from x = 2 to x = 9?
The average rate of change of the function f(x) = 1/x from x = 2 to x = 9 is -0.
3.
What is the average rate of change of the function f(x) = 1/x from x = 4 to x = 16?
The average rate of change of the function f(x) = 1/x from x = 4 to x = 16 is -0.
2.
What is the average rate of change of the function f(x) = 1/x from x = 8 to x = 32?
The average rate of change of the function f(x) = 1/x from x = 8 to x = 32 is -0.
1.
What is the average rate of change of the function f(x) = 1/x from x = 1 to x = 16?
The average rate of change of the function f(x) = 1/x from x = 1 to x = 16 is -0.
05.
What is the average rate of change of the function f(x) = 1/x from x = 1 to x = 32?
The average rate of change of the function f(x) = 1/x from x = 1 to x = 32 is -0.
025.
What is the average rate of change of the function f(x) = 1/x from x = 2 to x = 32?
The average rate of change of the function f(x) = 1/x from x = 2 to x = 32 is -0.
015625.
What is the average rate of change of the function f(x) = 1/x from x = 4 to x = 32?
The average rate of change of the function f(x) = 1/x from x = 4 to x = 32 is -0.
0078125.
What is the average rate of change of the function f(x) = 1/x from x = 8 to x = 32?
The average rate of change of the function f(x) = 1/x from x = 8 to x = 32 is -0.
00390625.
