Question

Arrange the functions in order from smallest rate of change (top) to greatest rate of change (bottom).

Function 1:+6
Function 2: +4
Function 3: −6
A) Function 1, Function 2, Function 3
B) Function 1, Function 3, Function 2
C) Function 2, Function 1, Function 3
D) Function 3, Function 1, Function 2

Answer 1

To determine the order from smallest to greatest rate of change, we compare the absolute values of the rates. Function 2 has the smallest rate (+4), followed by Function 1 (+6), and then Function 3 (−6) has the largest rate of change in magnitude. Therefore, the order is Function 2, Function 1, Function 3, which corresponds to Option C.

Step-by-step explanation:

To arrange the functions from the smallest rate of change to the greatest, we need to consider the numerical values provided. The rates of change for the functions are:

• Function 1: +6
• Function 2: +4
• Function 3: −6

It is important to note that a positive rate of change indicates an increase, while a negative rate of change indicates a decrease. The magnitude of change is irrespective of the direction (positive or negative), so we need only consider the absolute values of the rates of change. The absolute values are:

• Function 1: 6
• Function 2: 4
• Function 3: 6

Function 2 has the smallest absolute value, meaning the smallest rate of change. Function 1 and Function 3 both have the same magnitude of change, but since Function 3 is negative, it would typically be listed last when considering smallest to greatest. Thus, the correct order from smallest to greatest rate of change is:

1. Function 2: +4
2. Function 1: +6
3. Function 3: −6

So the correct answer is Option C: Function 2, Function 1, Function 3.