Answer:
Option B is the correct option.
Step-by-step explanation:
The given question is incomplete; complete question is attached herewith.
For this question we will evaluate each option one by one.
A). Function 1 has a greater rate of change by [tex]\frac{1}{4}[/tex]
Linear function 1. passes through two points (4, 0) and (0, -2).
Rate of change or slope of the line = [tex]\frac{y-y'}{x-x'}[/tex]
Slope m = [tex]\frac{0+2}{4-0}[/tex]
= [tex]\frac{1}{2}[/tex]
Rate of change or slope of the function (2) [tex]y=\frac{3}{4}x-2[/tex]
Slope m' = [tex]\frac{3}{4}[/tex]
m - m' = [tex]\frac{1}{2}-\frac{3}{4}=-\frac{1}{4}[/tex]
So function 2 has greater rate of change than function (1) by [tex]\frac{1}{4}[/tex]
Therefore, Option A is incorrect.
B). Function (2) has a greater rate of change by [tex]\frac{1}{4}[/tex]
As we have seen in the option (A) function 2 has the greater rate of change than function 2 by [tex]\frac{1}{4}[/tex]
Option (B) is correct.
C). Function (1) has a greater rate of change by [tex]\frac{1}{2}[/tex]
As proved above this option is incorrect.
D). Function (2) has a greater rate of change by [tex]\frac{1}{2}[/tex]
Option (D) is incorrect.
