Final answer:
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:
- Function 2: +4
- Function 1: +6
- Function 3: −6
So the correct answer is Option C: Function 2, Function 1, Function 3.