Question

Use the table to find the average rate of change of the function f(x) from the point (-1,2) to the point (3 1/2, 2)
X, f(x)
-1, 2
0, -1
1/2, 3
3 1/2, 2

Answer 1

To find the average rate of change of the function \( f(x) \) from the point \((-1, 2)\) to the point \((3 \frac{1}{2}, 2)\), you can use the following formula for the average rate of change:

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

In this case, let:

- \( a = -1 \)
- \( b = 3 \frac{1}{2} = \frac{7}{2} \)
- \( f(a) = f(-1) = 2 \)
- \( f(b) = f(3 \frac{1}{2}) = 2 \)

Now, substitute the values into the formula:

\[
\text{Average Rate of Change} = \frac{f(3 \frac{1}{2}) - f(-1)}{3 \frac{1}{2} - (-1)} = \frac{2 - 2}{\frac{7}{2} - (-1)}
\]

Calculating the denominator:

\[
\frac{7}{2} - (-1) = \frac{7}{2} + \frac{2}{2} = \frac{7 + 2}{2} = \frac{9}{2}
\]

So the average rate of change is:

\[
\text{Average Rate of Change} = \frac{0}{\frac{9}{2}} = 0
\]

Thus, the average rate of change of the function \( f(x) \) from the point \((-1, 2)\) to the point \((3 \frac{1}{2}, 2)\) is \( 0 \).