When we deal with functions, we should look for a range of definition of function and a set of values of function. The important component of the general algorithm of a research of function before creation of the schedule consists in it.
Instruction
1. For a start find a function range of definition. The range of definition includes all admissible arguments of function, that is such arguments at which function makes sense. It is clear, that in a denominator of fraction there cannot be zero, under a root there cannot be a negative number. The basis of a logarithm has to be positive and not equal to unit. Expression under a logarithm also has to be positive. Restrictions for a range of definition of function can be imposed also by a statement of the problem.
2. Analyze as the range of definition of function affects a set of values which function can accept.
3. The set of values of linear function represents a set of all real numbers (x belongs R) since the straight line set by the linear equation is infinite.
4. In case of square function find value of top of a parabola (x0=-b/a, y0=y(x0). If branches of a parabola are directed up (a> 0), then y0 will be a set of values of function all y>. If branches of a parabola are directed down (a <0), the set of values of function will be defined by inequality of y
5. A set of values of cubic function - a set of real numbers (x belongs R). In general, a set of values of any function with an odd exponent (5, 7...) is area of real numbers.
6. A set of values of an exponential function (y=a^x where an is positive number) - all numbers more than zero.
7. For finding of a set of values of linear-fractional or fractional and rational function it is necessary to find the equations of horizontal asymptotes. Find such values x at which the denominator of fraction addresses in zero. Imagine how the schedule will look. Construct the sketch of the schedule. On the basis of it define a set of values of function.
8. The set of values of trigonometrical functions of a sine and cosine is strictly limited. The sine and a cosine on the module cannot exceed units. And here the value of a tangent and cotangent can be any.
9. If it is required to find a set of values of function on the set piece of values of an argument in a task, consider function specifically on this piece.
10. When finding a set of values of function it is useful to define intervals of monotony of function - increase and decrease. It allows to understand the nature of behavior of function.