The exponent of a linear function is 1.
A linear function is a type of polynomial function. The defining characteristic of a linear function, as stated in the provided reference, is that the highest exponent of the variable is 1. This means that the variable in a linear function is raised to the power of 1 (which is often not explicitly written).
Understanding Linear Functions
To further clarify, let's break down the standard form of a linear function:
-
Standard Form: y = mx + b
- y: Represents the dependent variable.
- m: Represents the slope of the line.
- x: Represents the independent variable. Notice that 'x' has an implied exponent of 1 (x1).
- b: Represents the y-intercept.
Examples of Linear Functions
Here are some examples of linear functions to illustrate the exponent:
- y = 2x + 3 (Exponent of x is 1)
- f(x) = -x + 5 (Exponent of x is 1)
- y = 7x (Exponent of x is 1)
In each of these examples, the variable 'x' is raised to the power of 1, making them linear functions.
