Content deleted Content added
m clean up equation and {{math}} segments (via WP:JWB) |
→Properties: Added about b=0, homogeneous and affine |
||
Line 14:
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 exactly 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.
If <math>b=0</math> then the linear function is said to be ''homogeneous''. Such function defines a line that passes through the origin of the coordinate system, that is, the point <math>(x,y)=(0,0)</math>. In advanced mathematics texts, the term ''linear function'' often denotes specifically homogeneous linear functions, while the term [[affine function]] is used for the general case, which includes <math>b\neq0</math>.
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.
| |||