Question

Given the function f(x) = 3x - 5, how much does f(x) change if x decreases by 2?

A) f(x) will increase by 1
B) f(x) will decrease by 11
C) f(x) will decrease by 6
D) f(x) will increase by 6

Answer 1

When x decreases by 2 in the function f(x) = 3x - 5, f(x) will decrease by 6.

Step-by-step explanation:

To find out how much the function f(x) = 3x - 5 changes when x decreases by 2, we need to substitute the new value of x into the function and calculate the difference.

When x decreases by 2, the new value of x becomes x - 2. So, the new function becomes f(x - 2) = 3(x - 2) - 5.

Expanding this equation, we get f(x - 2) = 3x - 6 - 5 = 3x - 11.

To calculate the change in the function, we subtract the original function f(x) from the new function f(x - 2):

f(x - 2) - f(x) = (3x - 11) - (3x - 5) = -11 - (-5) = -11 + 5 = -6.

Therefore, the correct answer is C) f(x) will decrease by 6.

Answer 2

When x in the function f(x) = 3x - 5 decreases by 2, the value of f(x) decreases by 6. This is found by evaluating the difference between f(x) and f(x - 2), leading to the conclusion that the correct answer is C) f(x) will decrease by 6.

This correct answer is C)

Step-by-step explanation:

The question asks how much the value of the function f(x) = 3x - 5 changes if the independent variable x decreases by 2.

Let's calculate the value of f(x) before and after the decrease:

• Initially: f(x) = 3x - 5
• After a decrease of 2 in x: f(x - 2) = 3(x - 2) - 5 = 3x - 6 - 5 = 3x - 11

The change in f(x) as x decreases by 2 is the difference f(x) - f(x - 2), which is:

(3x - 5) - (3x - 11) = 3x - 5 - 3x + 11 = 6

Therefore, the value of f(x) will decrease by 6 when x decreases by 2. The correct answer is C) f(x) will decrease by 6.

This correct answer is C)