what is the rate of change of the function shown on the graph? round to the nearest tenth. 2.00 2.50 5.25…

Explanation:

Step1: Recall rate - of - change formula

The rate of change of a function between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. We can use the points $(1,5)$ and $(2,12.5)$.

Step2: Substitute values into formula

Let $(x_1,y_1)=(1,5)$ and $(x_2,y_2)=(2,12.5)$. Then $m=\frac{12.5 - 5}{2 - 1}$.

Step3: Calculate the rate of change

$m=\frac{7.5}{1}=7.5$. But if we use the points $(0,2)$ and $(1,5)$: $m=\frac{5 - 2}{1 - 0}=\frac{3}{1}=3$. Using the points $( - 1,0.8)$ and $(0,2)$: $m=\frac{2 - 0.8}{0-( - 1)}=\frac{1.2}{1}=1.2$. Averaging these rates of change over small intervals is not the best way. Using the two - point formula with $(1,5)$ and $(2,12.5)$ gives $m = 7.5$ which is not in the options. Let's use the secant line approximation more generally. If we consider the overall trend and use the points $(0,2)$ and $(2,12.5)$: $m=\frac{12.5 - 2}{2 - 0}=\frac{10.5}{2}=5.25$.

Answer:

5.25