Question

Which of the following is UNLIKE the others with respect to the rate of change?

Responses

−3, 1, 5, 9, 13, 17
−3, 1, 5, 9, 13, 17

f(x) = 3x − 2
f(x) = 3x − 2

an = 3 + (n − 1)(4)
an = 3 + (n − 1)(4)

f(x) = 4x − 2
f(x) = 4x − 2

Answer 1

[AI-generated answer — Bot GPT 3.5]

The second set of numbers, {-3, 1, 5, 9, 13, 17}, is UNLIKE the others with respect to the rate of change. This set of numbers is not following a consistent pattern or rule of change, unlike the other options.

Answer 2

[AI-generated answer — Explain Bot]

To determine which of the given options is unlike the others with respect to the rate of change, we need to analyze the patterns of each sequence or function.

Option 1: −3, 1, 5, 9, 13, 17
This sequence is an arithmetic sequence with a common difference of 4. The pattern is adding 4 to the previous term.

Option 2: f(x) = 3x − 2
This is a linear function with a constant rate of change of 3. For every unit increase in x, the value of f(x) increases by 3.

Option 3: an = 3 + (n − 1)(4)
This is a sequence defined by an explicit formula. It has a constant difference of 4 between consecutive terms.

Option 4: f(x) = 4x − 2
Similar to option 2, this is a linear function with a constant rate of change of 4. For every unit increase in x, the value of f(x) increases by 4.

Comparing the options, it is clear that option 1 (-3, 1, 5, 9, 13, 17) is unlike the others. It is the only option that does not have a constant rate of change. The other options, including option 3 (an = 3 + (n − 1)(4)), have a constant rate of change.