Question

Considering only functions with a greater rate of change than that of the function represented on the graph, which function has the lowest rate of change?​

Answer 1

Answer:

Step-by-step explanation:

The rate of change is a just a fancy name for slope.

First let's calculate the slope of the line in the graph.

We see it passes through the points (3,2) and (0,-2), so the slope is:

$S = \frac{2 - -2}{3 - 0} = \frac{4}{3}$

So the reference slope is 4/3.

Next step is to identify, among the proposed solutions, the one that have a steepest slope than 4/3 (1.33).  In the equations, the slope is the coefficient of the x element.

A. 13/7 - Greater than 4/3?  Yes (1.86)

B. 7/5 - Greater than 4/3?  Yes (1.4)

C. 11/8 - Greater than 4/3?  Yes (1.375)

D. 5/4 - Greater than 4/3?  No (1.25)

E. 5/3 - Greater than 4/3?  Yes (1.66)

So, only D (5/4) is smaller than 4/3.  Among the 4 others, which one has the lowest slope?

11/8 has the lowest slope that is higher than 4/3.