Which of the following represents a linear function?

A linear function is defined as one that can be graphed as a straight line in a coordinate system. The general form of a linear function is expressed as f(x) = mx + b, where 'm' is the slope and 'b' is the y-intercept.

In the case of the correct choice, f(x) = ax + b fits this definition perfectly. In this expression, 'a' (the coefficient of x) represents the slope of the line, and 'b' is the value where the line intersects the y-axis. Such a function demonstrates a constant rate of change, which is the hallmark of linearity.

Other choices represent different types of functions and do not exhibit the properties of a linear function. For instance, f(x) = a is a constant function, which does not change with different values of x and therefore does not produce a line with varying slope. The function f(x) = ax^2 + bx + c represents a quadratic function, which displays a parabolic shape rather than a straight line. Finally, f(x) = K/x is a rational function that creates a hyperbolic curve and is characterized by its asymptotic behavior rather than linearity. Thus, only the expression f