Definition:Linear Function

Definition

A linear function is a polynomial whose degree is $1$:

One Variable

A linear function of one variable has the form:

$\map f x = a_0 + a_1 x$

where $a_0$ and $a_1$ are constants.

Two Variables

A linear function of two variables has the form:

$\map f {x, y} = a_0 + a_1 x + a_2 y + a_3 x y$

where $a_0$, $a_1$, $a_2$ and $a_3$ are constants.

Also known as

A linear function is also known as a linear polynomial.

Also see

• Results about linear functions can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): linear function
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): polynomial
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): linear function
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): polynomial