The tables above list some of the values of three functions, f, g, and h. Which of the three functions could be a linear function?

Rationale

Both functions f and h could be linear functions.

To determine which functions could be linear, one must analyze the relationships between the inputs and outputs of each function. A linear function produces a constant rate of change, which can be observed through the values provided in the tables for f and h.

A (f only) YOUR ANSWER

While function f appears to have a consistent pattern suggesting linearity, dismissing function h overlooks its potential to also exhibit a linear relationship. Given that both functions f and h could be linear, this choice is incomplete.

B (g only) YOUR ANSWER

Function g shows inconsistencies in the rate of change between its values, indicating a non-linear relationship. Therefore, it cannot be classified as linear, making this choice incorrect.

C (h only) YOUR ANSWER

Similar to function f, function h displays a consistent pattern in its values that may suggest linearity. However, this choice fails to recognize that function f also has the potential to be linear, so it is not fully accurate.

D (f and h only) CORRECT

Both functions f and h demonstrate a constant rate of change between their respective inputs and outputs, fulfilling the criteria for linear functions. This option correctly identifies both functions as potentially linear.

E (f, g, and h) YOUR ANSWER

Function g does not maintain a constant rate of change, thereby disqualifying it from being linear. This choice incorrectly includes g, leading to an inaccurate conclusion about the nature of the functions.

Conclusion

In summary, functions f and h can both be classified as linear due to their consistent rate of change observed in the data provided. Function g, however, fails to meet this criterion, thereby excluding it from being a linear function. Understanding the characteristics of linearity is crucial for analyzing function behavior in various mathematical contexts.

The tables above list some of the values of three functions, f, g, and h. Which of the three functions could be a linear function?

Both functions f and h could be linear functions.

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