Question

If x represents time, the average rate of change of the function f(x) in the first three seconds is ___.

Answer 1

Answer

If x represents time, the average rate of change of the function f(x) in the first three seconds is -50.

Explanation

The average rate of change of a linear function is the slope of the liner function. To find the slope of our linear function, we are using the slope formula:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

where

$m$ is the slope of the line

$(x_{1},y_{1})$ are the coordinates of the first point on the line

$(x_{2},y_{2})$ are the coordinates of the second point

From our graph we can get the points (0, 150) and (3, 0), so $x_{1}=0$, $y_{1}=150$, $x_{2}=3$, and $y_{2}=0$. Let's replace the values in our formula to find the slope of our linear function:

$m=\frac{0-150}{3-0}$

$m=\frac{-150}{3}$

$m=-50$

Since the average of change a linear function is equal to its slope, the average rate of change of the function in the first three seconds is -50