Question

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

Answer 1

Answer:

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)

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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.

Answer 2

Answer: Fourth option

$m=2$

Step-by-step explanation:

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

$m=\frac{f(x_2)-f(x_1)}{x_2-x_1}$

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

$m=\frac{5-3}{2-1}$

$m=\frac{2}{1}$

$m=2$