Y function graph = f (x) is a set of all points of the plane, coordinate x at which satisfy to y ratio = f (x). The function graph visually illustrates behavior and properties of function. For creation of the schedule several values of an argument usually are chosen x and for them the corresponding values of the y=f (x) function are calculated. For more exact and evident creation of the schedule it is useful to find its points of intersection with axes of coordinates.
Instruction
1. To find a function graph point of intersection with axis y, it is necessary to calculate value of function at x =0, i.e. to find f(0). For an example we will use a linear function graph, represented in fig. 1. Its value at x =0 (y=a*0+b) is equal to b, therefore, the schedule crosses ordinate axis (axis Y) in a point (0, b).
2. When crossing abscissa axis (axis X) the value of function is equal 0, i.e. y=f(x)=0. For calculation x it is necessary to solve the equation of f (x) =0. In case of linear function we receive ax+b=0 equation from where we find x=-b/a. Thus, axis X is crossed in a point (-b/a, 0).
3. In more difficult cases, for example, in case of square dependence of y from x, the equation of f (x) =0 has two roots, therefore, abscissa axis is crossed twice. In case of periodic dependence of y from x, for example y=sin(x), its schedule has infinite number of points of intersection with axis X. For check of correctness of finding of coordinates of points of intersection of a function graph with axis X it is necessary to substitute the found values x in expression of f (x). The value of expression at any of calculated x has to be equal to 0.