Question

What is the consent rate of change of the function represented in the table?

Answer 1

Hello there. To solve this question, we'll have to remember some properties about slope of a line.

In order to find the constant rate of change of the function represented in the table below, we first have to remember why does it means that the function is a line.

Knowing the instantaneous rate of change of a function f(x) is given by its derivative, i. e.

`f^(\prime)(x)`

And say this rate of change is constant, that is

`f^(\prime)(x)=A`

Integrating both sides of the equation with respect to x, we have that:

`\begin{gathered} \int f^(\prime)(x)dx=\int Adx \\ \\ f(x)=Ax+B \end{gathered}`

Where A and B are constants, therefore f(x) is the equation of a line.

In fact, this constant rate of change is the slope of the line, so we simply need to find it.

Given two points (x0, y0) and (x1, y1) from the equation of a line, we can find its slope m by using the following formula:

`m=(y_1-y_0)/(x_1-x_0)`

Taking two points from the table, say (-1, 7) and (3, -9), we plug in the formula to find:

`m=(-9-7)/(3-(-1))=(-16)/(4)=-4`

Therefore the slope of this line, and constant rate of change of this function is equal to -4 and it is the answer contained in the option H.