Question

Select all the correct locations on the table.

Answer 1

The desired average rate of change is -60.

Consider the first and the last point of the table.

These points are (1, 27) and (5, -213)

The rate of change of a function is given as:

$\frac{f( x_{2} )-f( x_{1} )}{ x_{2} - x_{1} }$

x₂ is the last point and x₁ is the first point. Using the values we get:

$\frac{-213-27}{5-1} \\ \\ = \frac{-240}{4} \\ \\ =-60$

This means, the first and the last point give an average rate of change of -60.

Answer 2

Be $y=f(x)$, a rate of change is defined by the following equation:

$\frac{\Delta y}{\Delta x}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

So, the problem establishes that we need to find out two points with an average rate of -60. So, the table above shows five points. Hence, we will take two of them, say:

$P_{1}(1, 27)$
$P_{2}(5, -213)$

Therefore:

$\frac{\Delta y}{\Delta x}=\frac{-213-27}{5-1}=\boxed{-60}$

So these two points are the ones we were looking for.