What are linear functions characterized by?

Linear functions are characterized by the fact that all variables appear in separate terms and are raised only to the first power. This is a fundamental property of linearity in a function. In a linear function, the relationship between the independent and dependent variables can be expressed as a straight line when graphed on a coordinate system. The general form of a linear function is typically represented as ( y = mx + b ), where ( m ) is the slope and ( b ) is the y-intercept.

Since the variables are raised only to the first power, their graphs do not involve any curves, which distinguishes linear functions from polynomial or non-linear functions. Moreover, the coefficients of the variables can take any value (positive, negative, or zero), but the essential defining characteristic is the first power.

This definition effectively excludes the other options. For instance, raising variables to any power would lead to non-linear functions, and requiring variables to be multiplied together or restricting them to be only negative do not reflect the traits of linearity in a function. Thus, the correct understanding of linear functions aligns perfectly with the description provided in the chosen answer.