Coordinate systems, linear functions

      -Each function can be plotted in a coordinate system.

      -The best  known coordinate system is the cartesian one, named after Descartes.

      -This kind of coordinate sytem consists of two mutually perpendicular coordinate axes whose intersection point is called the origin.

      -The vertical axis is called the y-axis while the horizontal axis is called the x-axis.

      -The coordinate system divides the plane into four equal quadrants.

      -Every point of the plane can be represented by its coordinates.

      -Coordinates are used to mark the points.

      -A point is given int he form of P(x;y). The value of x always comes first.

      -Def.: lett he function f:A→B, f(x)=mx+b (m and b are constants) be given. The function f is called a linear function.

      -if m=0 then the function f(x)=b is a straight line which is perpendicular to the y-axis (or parallel with x-axis)

      A special case of linear functions is f(x)=mx. It is called a function of direct proportionality. The graph of f(x)=mx is a straight line which passes through the origin.

      Any function whose graph is a straight line is called a linear function. They are also called the functions of the first degree.

      In function f(x)=mx+b m is called a gradient (which can be either positive or negative), b is called an intercept of the y-axis.

      To draw a straight line graph only two points need to be known. Once these have been plotted, the line can be drawn between them and extended if necessary of both ends.

 

2012.03.02.

Oldal: Coordinate systems, linear functions
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