Linear function (calculus): Difference between revisions

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Such a function is called ''linear'' because its [[graph of a function|graph]], the set of all points <math>(x,f(x))</math> in the [[Cartesian plane]], is a [[line (geometry)|line]]. The coefficient ''a'' is called the ''slope'' of the function and of the line (see below).

If the slope is <math>a=0</math>, this is a ''constant function'' <math>f(x)=b</math> defining a horizontal line, which some authors exclude from the class of linear functions.<ref>{{harvnb|Swokowski|1983|loc=p. 34}}</ref> With this definition, the degree of a linear polynomial would be exacxxxxtlyexactly one, and its graph would be a line that is neither vertical nor horizontal. However, in this article, <math>a\neq 0</math> is required, so constant functions will be considered linear.

The natural [[Domain of a function|___domain]] of a linear function <math>f(x)</math>, the set of allowed input values for {{math|''x''}}, is the entire set of [[real number]]s, <math>x\in \mathbb R.</math> One can also consider such functions with {{math|''x''}} in an arbitrary [[field (mathematics)|field]], taking the coefficients {{math|''a, b''}} in that field.