Mathematics: Consider the two functions. Which statement is true? A) Function 1 has a greater rate of change by 1 4 B) Function 2 has a greater rate of change by 1 4 C) Function 1 has a greater rate of change by 1 2 D) Function 2 has a greater rate of change by 1 2

The answer is C. x=In(5/3)-2 Step-by-step explanation:...

Consider the two functions. Which statement is

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20.01.2022

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 $\frac{1}{4}$

Linear function 1. passes through two points (4, 0) and (0, -2).

Rate of change or slope of the line = $\frac{y-y'}{x-x'}$

Slope m = $\frac{0+2}{4-0}$

= $\frac{1}{2}$

Rate of change or slope of the function (2) $y=\frac{3}{4}x-2$

Slope m' = $\frac{3}{4}$

m - m' = $\frac{1}{2}-\frac{3}{4}=-\frac{1}{4}$

So function 2 has greater rate of change than function (1) by $\frac{1}{4}$

Therefore, Option A is incorrect.

B). Function (2) has a greater rate of change by $\frac{1}{4}$

As we have seen in the option (A) function 2 has the greater rate of change than function 2 by $\frac{1}{4}$

Option (B) is correct.

C). Function (1) has a greater rate of change by $\frac{1}{2}$

As proved above this option is incorrect.

D). Function (2) has a greater rate of change by $\frac{1}{2}$

Option (D) is incorrect.

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