Function which back indicative is called logarithmic. Such function has an appearance: y = logax in which the value a is positive number (not equal to zero). The appearance of the schedule of logarithmic function depends on value a.
It is required to you
- - mathematical reference book;
- - ruler;
- - simple pencil;
- - notebook;
- - handle.
Instruction
1. Before starting creation of the schedule of logarithmic function pay attention that the set of positive numbers is a range of definition of this function: this size is designated by R+. At the same time, logarithmic function has an area of value which is presented by real numbers.
2. Attentively study task conditions. If a> 1, on graphics represent the increasing logarithmic function. It is simple to prove such feature of logarithmic function. For an example, take two any positive x1 and x2 values, and, x2> to x1. Prove that loga x2> loga x1 (it is possible to make it method by contradiction).
3. Assume that loga x2≤loga x1. Considering that the exponential function of a look at = ah at value a> 1 increases, inequality will take the following form: aloga x2≤aloga x1. By well-known definition of a logarithm of aloga x2=x2, while aloga x1=x1. So, inequality takes a form: x2≤x1, and it directly contradicts initial assumptions, in consent with which x2> x1. Thus, you came to that, as was to be shown: at a> 1 logarithmic function increases.
4. Represent the schedule of logarithmic function. Y function graph = will pass logax through a point (1;0). If a> 1, function is increasing. Therefore, if 0