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Which of the following is UNLIKE the others with respect to the rate of change (common difference)?

Responses

2, 6, 10, 14, 18

f(x) = 6x − 2

f(x) = 6x +1

an = −5 + 6(n − 1)

User ElHacker
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1 Answer

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Explanation:

The set of numbers 2, 6, 10, 14, 18 represents an arithmetic sequence with a common difference of 4.

The function f(x) = 6x - 2 represents a linear function with a slope (rate of change) of 6. This means that for each increase of 1 in x, the function's output (y) increases by 6.

The function f(x) = 6x + 1 also represents a linear function, but its rate of change (slope) is 6, just like the previous function.

The sequence an = -5 + 6(n - 1) represents an arithmetic sequence with a common difference of 6. It's essentially the same as the first set of numbers (2, 6, 10, 14, 18), just written in a different form.

So, when we consider the rate of change (common difference), all options (1, 2, and 4) are alike because they have a common difference of 4 or 6. Option 3, f(x) = 6x + 1, is unlike the others because it has a different rate of change (slope) of 6, whereas the rest have a common difference of 4 or 6.

User Timanderson
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