Question

which expression can be used to determine the average rate of change in $f(x)$ over the interval $2, 9$? options: $f(9 - 2)$, $\frac{f(9 - 2)}{9 - 2}$, $f(9) - f(2)$, $\frac{f(9) - f(2)}{9 - 2}$. (graph of $f(x)$ on a coordinate grid with x - axis from 0 to 10 and y - axis from 0 to 10, showing a red curve.)

Explanation:

Step1: Recall average rate of change formula

The average rate of change of a function \( f(x) \) over the interval \([a, b]\) is given by the formula \(\frac{f(b)-f(a)}{b - a}\).

Step2: Identify \( a \) and \( b \) for the interval \([2, 9]\)

Here, \( a = 2 \) and \( b = 9 \). Substituting these values into the formula, we get \(\frac{f(9)-f(2)}{9 - 2}\).

Answer:

\(\frac{f(9)-f(2)}{9 - 2}\) (the fourth option)