consider the graph of $f(x)$.\nwhat is the average rate of change of $f(x)$ from $x_1 = 4$ to $x_2 = 7$…

Explanation:

Step1: Identify the coordinates for the given x-values

From the graph, at $x_1 = 4$, the point is $(4, 10)$, so $f(4) = 10$. At $x_2 = 7$, the point is $(7, 11)$, so $f(7) = 11$.

Step2: Apply the average rate of change formula

The average rate of change is calculated using the formula: $$m = \frac{f(x_2) - f(x_1)}{x_2 - x_1}$$

Step3: Substitute the values into the formula

Substitute the identified coordinates into the expression: $$m = \frac{11 - 10}{7 - 4}$$

Step4: Simplify the fraction

Calculate the differences in the numerator and denominator: $$m = \frac{1}{3}$$

Answer:

1/3