what is the rate of change of the function shown on the graph? round to the nearest tenth\n2.00\n2.50\n5.25\n…

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 $\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Select two points

Let's take the points $(1,5)$ and $(2,12.5)$. Here $x_1 = 1,y_1 = 5,x_2=2,y_2 = 12.5$.

Step3: Calculate rate of change

Substitute the values into the formula: $\frac{12.5 - 5}{2 - 1}=\frac{7.5}{1}=7.5$. But if we take the points $(0,2)$ and $(1,5)$: $\frac{5 - 2}{1 - 0}=\frac{3}{1}=3$. If we take $(1,5)$ and $(2,12.5)$: $\frac{12.5-5}{2 - 1}=7.5$. Averaging these (since we want an overall rate of change approximation) is not the best way. Let's use the most "linear - like" part. Using $(1,5)$ and $(2,12.5)$ gives $\text{Rate of change}=\frac{12.5 - 5}{2 - 1}=7.5$. However, if we consider the secant line between $(0,2)$ and $(2,12.5)$: [ \begin{align*} \text{Rate of change}&=\frac{12.5 - 2}{2-0}\ &=\frac{10.5}{2}\ & = 5.25 \end{align*} ]

Answer:

5.25