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

2

Step-by-step 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)

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.

Fourth option

Step-by-step explanation:

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

In this case the function is the line shown in the graph. Then we look for the values of for and

When then

When then

Therefore

3 is greater then both of those numbers