what is the rate of change of the function shown on the graph? round to the nearest tenth\n(2, 12.5)\n(1…

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 $\frac{y_2 - y_1}{x_2 - x_1}$. Let's use the points $(1,5)$ and $(2,12.5)$.

Step2: Substitute values into formula

Here, $x_1 = 1,y_1 = 5,x_2=2,y_2 = 12.5$. Then $\frac{y_2 - y_1}{x_2 - x_1}=\frac{12.5 - 5}{2 - 1}$.

Step3: Calculate the result

$\frac{12.5 - 5}{2 - 1}=\frac{7.5}{1}=7.5$. But if we use the points $(0,2)$ and $(1,5)$: $\frac{5 - 2}{1 - 0}=\frac{3}{1}=3$. Using the points $( - 1,0.8)$ and $(0,2)$: $\frac{2 - 0.8}{0-( - 1)}=\frac{1.2}{1}=1.2$. A more accurate way for a non - linear function is to consider the average rate of change over a small interval. Let's use the points $(1,5)$ and $(2,12.5)$ again. The rate of change $\frac{12.5 - 5}{2 - 1}=7.5$. If we assume we want an approximation and consider the general trend, we can also calculate the average rate of change between multiple pairs of points. Let's take two adjacent points $(1,5)$ and $(2,12.5)$: The rate of change formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting $x_1 = 1,y_1 = 5,x_2 = 2,y_2=12.5$ gives $m=\frac{12.5 - 5}{2 - 1}=7.5$. If we consider a different pair of points say $(0,2)$ and $(1,5)$ the rate of change is $\frac{5 - 2}{1-0}=3$. Averaging these two rates of change (a simple approximation method for non - linear functions) $\frac{7.5 + 3}{2}=5.25$.

Answer:

5.25