Question

Find the average rate of change for the given function from x = 1 to x = 2.

1) -2
2) -1/2
3) 1/2
4) 2

Answer 1

Answer: Fourth option

`m=2`

Explanation:

If we call m the average change rate of a function between
`x_1` and
`x_2`, then, by definition:

`m=(f(x_2)-f(x_1))/(x_2-x_1)`

In this case the function is the line shown in the graph. Then we look for the values of
`y = f (x)` for
`x = 1` and
`x = 2`

When
`x=1` then
`f(x)=3`

When
`x=2` then
`f(x)=5`

Therefore

`m=(5-3)/(2-1)`

`m=(2)/(1)`

`m=2`

Answer 2

2

Explanation:

The average rate of change from x=1 to x=2 is the same as finding the slope of a line at x=1 and x=2.

So we are going to need to corresponding y coordinates.

What y corresponds to x=1? y=3

What y corresponds to x=2? y=5

So we have the ordered pairs (1,3) and (2,5).

Line the points up vertically and subtract vertically then put 2nd difference over 1st difference.

(2 , 5)

-(1 , 3)

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1 2

The average rate of change is 2/1 or just 2.

Now since we were asked to find the average rate of change given the function was a line, it really didn't matter what two points you used on that line.