Which of the following best describes a linear function?

Prepare for the TAMU MATH140 Mathematics Exam with study tools including flashcards and multiple choice questions. Each question comes with hints and explanations to help you excel. Get ready for your final exam!

A linear function is best described as a function that graphs as a straight line. This characteristic of linear functions is derived from their standard form, which is typically written as (y = mx + b), where (m) represents the slope and (b) the y-intercept. Because of this linearity, the graph of such a function will always produce a straight line when plotted on a coordinate plane.

In contrast, a function with a quadratic equation will graph as a parabola, which is distinctly non-linear due to its curvature. Functions that oscillate between different values are periodic, such as sine or cosine functions, and do not display a linear relationship, instead offering a wave-like graph. Lastly, functions defined by a polynomial of degree three or higher are classified as cubic or higher-degree polynomials, and they can exhibit intricate behaviors, such as multiple turning points and inflection points, rather than representing a straightforward slope associated with linear functions. Thus, the defining characteristic of a linear function is its ability to produce a straight line when graphed, reinforcing the correctness of the chosen answer.

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