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?
Functions f and h could be linear functions.
Both functions f and h display a consistent rate of change between their values, indicating that they can be represented by linear equations. In contrast, function g exhibits a non-linear pattern, suggesting that it does not meet the criteria for linearity.
While function f does demonstrate a consistent rate of change, suggesting it could be linear, this choice ignores the possibility that function h also maintains a linear behavior. Therefore, this option is incomplete, as it excludes another valid function that could be linear.
Function g does not show a constant rate of change; instead, it exhibits a curvilinear pattern, indicating it is not a linear function. Thus, this choice is incorrect, as function g cannot be classified as linear based on the provided values.
Though function h appears to have a consistent rate of change and could therefore be linear, this choice ignores function f, which also meets the criteria for linearity. Hence, this option is inaccurate because it overlooks another function that also qualifies as linear.
Both functions f and h exhibit a constant rate of change, qualifying them as potential linear functions. This option accurately reflects the behaviors of both functions and correctly identifies that they can be represented by linear equations.
This choice incorrectly includes function g, which has a non-linear pattern. While functions f and h could be linear, including g disqualifies this option due to its deviation from linear characteristics.
In determining which functions could be linear, it is essential to examine their rates of change. Functions f and h both demonstrate a consistent increase or decrease, which is indicative of linearity. Function g, on the other hand, does not exhibit this property, confirming that only f and h could be classified as linear functions.
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