Which of the following describes a linear function?

Which of the following describes a linear function?

• A. A function that creates a U-shape on a graph
• B. A function that has a constant rate of change
• C. A function that is defined by a quadratic equation
• D. A function that cannot be represented with a graph

Answer: (B)

A linear function is defined as one that has a constant rate of change, which translates graphically to a straight line. This means that for any two points on the graph of a linear function, the change in the y-values divided by the change in the x-values (often referred to as the slope) remains the same, regardless of which two points are chosen. In a linear equation of the form \(y = mx + b\), \(m\) represents the slope (the constant rate of change), and \(b\) is the y-intercept. This highlights how, as the input (x) changes, the output (y) changes at a consistent and predictable rate. Thus, the essence of linear functions is this linearity, characterized by their predictable behavior in their rates of change, which distinctly sets them apart from non-linear functions. Functions that create a U-shape on a graph refer to quadratic functions, which exhibit variable rates of change and curvature. A quadratic equation typically has the form \(y = ax^2 + bx + c\) and can have either maximum or minimum points, thereby not maintaining a constant rate of change. Additionally, functions defined by quadratic equations are classified as non-linear. The notion that a function

A linear function is defined as one that has a constant rate of change, which translates graphically to a straight line. This means that for any two points on the graph of a linear function, the change in the y-values divided by the change in the x-values (often referred to as the slope) remains the same, regardless of which two points are chosen.

In a linear equation of the form (y = mx + b), (m) represents the slope (the constant rate of change), and (b) is the y-intercept. This highlights how, as the input (x) changes, the output (y) changes at a consistent and predictable rate. Thus, the essence of linear functions is this linearity, characterized by their predictable behavior in their rates of change, which distinctly sets them apart from non-linear functions.

Functions that create a U-shape on a graph refer to quadratic functions, which exhibit variable rates of change and curvature. A quadratic equation typically has the form (y = ax^2 + bx + c) and can have either maximum or minimum points, thereby not maintaining a constant rate of change. Additionally, functions defined by quadratic equations are classified as non-linear. The notion that a function