Question 13

f and h could be linear functions.

Both functions f and h exhibit a consistent rate of change across the provided values, indicating that they could represent linear relationships. In contrast, function g does not maintain a constant rate of change, which is characteristic of linear functions.

A) f only

This option is incorrect because although function f may exhibit linear characteristics, it does not account for the possibility that function h could also be linear. Both functions f and h need to be considered for a complete answer.

B) g only

Function g is not a linear function, as it lacks a constant rate of change between its values. This variability indicates that g cannot fit the criteria for a linear function.

C) h only

While function h may appear linear based on its values, selecting this option disregards the fact that function f also satisfies the conditions for being linear. Therefore, this option is incomplete.

D) f and h only

This is the correct answer because both functions f and h demonstrate a consistent rate of change, suggesting they could represent linear functions. This option acknowledges that both functions meet the criteria necessary for linearity.

E) f, g, and h

This option is incorrect because, while functions f and h may be linear, function g does not maintain a constant rate of change and therefore cannot be classified as a linear function.

Conclusion

The correct answer identifies that both functions f and h could be linear, as they demonstrate a constant rate of change. In contrast, function g fails to meet the criteria for linearity, making options that include g incorrect. Thus, f and h are the only functions that align with the properties of linear functions.