Question

Use the average rate of change to describe the graph f(x) with the points (0, 0), (1, 1), (4, 2) over the interval [1,4]
1. the average rate of change is 1/3
2. the average rate of change is 3
3. the average rate of change is -1/3
4. the average rate of change is 1

Answer 1

To find the average rate of change of the function \( f(x) \) over the interval \([1, 4]\), we use the formula:

\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]

where \( a = 1 \) and \( b = 4 \).

From the given points, we have \( f(1) = 1 \) and \( f(4) = 2 \).

Now we can plug these values into the formula:

\[
\text{Average Rate of Change} = \frac{f(4) - f(1)}{4 - 1} = \frac{2 - 1}{4 - 1} = \frac{1}{3}
\]

Thus, the average rate of change over the interval \([1, 4]\) is:

1. the average rate of change is \( \frac{1}{3} \)

So the correct answer is **1. the average rate of change is \( \frac{1}{3} \)**.