Linear function, graph of a linear function

Definition: a Linear function is a function of the form where is some number

Properties of linear functions

1. Scope



2. Multiple value

when

when

3. Parity, odd parity

if the function is neither even nor odd

in — steamroom

if and is odd

4. The point of intersection with the axes

at the point of intersection with the axis

then straight and parallel to the axis at a and coincides with the axis when

5. Continuity and differentiability

A linear function is continuous and diferencian on the entire number line

6. The increase and decrease of

when a function is increasing on all number line

when a function is decreasing on the entire number line

when a function became

7. The graph of a linear function is always a straight, tangent of slope angle of this straight line to the axis

   at the point of intersection with the axis

   — the angular coefficient of the straight

   when is a straight line passing through the origin

   when is a straight line, not passing through the origin

Graphs of linear functions