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Math tutor online will help to deal with the issue of the definition of the function.

Function scope

The scope is the value of a variable that can accept any function. If you specify a function as y = f(x). The domain of the function definition is all the possible x at which y exists. These are the values of x that can be substituted into the given equation y = f(x). Denote the domain of D(y). Therefore, D(y) or D(f) is the domain of numbers on which the function is set.


First, what is the function? Tutor in mathematics and physics helps children or students to deal with any unclear question, and especially with the topic of the function. It must be remembered that first of all it is a dependence. Depend on the value of the function on the variable. It depends on x. The dependencies between these variables (y and x) are called functional.

The function has the form y = f(x) (y – the value of the function, x – the argument).

Recall which basic elementary functions should pay attention to :

1. The linear function y=kx+b, k,b – coefficients. The graph is a line.

2. Inverse proportionality y=k/x, k – coefficient. Graph – hyperbola.

3. The function of the square root y= x. The graph is a branch of the parabola, only oriented not upwards, but to the right.

Math tutor online will tell other materials on the main features of elementary functions.

Function definition study

It is now possible to explore the scope of these functions. In order to better understand and systematize the information, let’s present the algorithm of finding the scope of the definition in tabular form. An online tutor in mathematics in the 9th grade should tell you how the scope of the function definition and the scope of the function values are different.

First Step.

Looking at the function, you need to ask yourself the question «What can not be?».

  • If you have a linear function, then there can be all the possible x. That is, x can be any x, at any variable x there will be y.
  • If you have a type function – inverse proportionality, pay attention to the denominator. It cannot be 0. Why can’t the denominator be 0? Because in terms of the school curriculum we cannot divide by 0. The risk of fraction shows us division. Then we point out that x at which the denominator is 0 cannot be in our domain of function definition.
  • If you have a square root function, note that a subzero expression can never be a negative number. We can say that the sublimated expression can only be more than 0 or equal to 0. We conclude that x, at which the sublimated expression will have a negative value is impossible.

Second step.

Analyzing the expressions we have conditions for.

  • If the function of type is inversely proportional, then the denominator cannot be 0. To find x of which cannot be, we equate the denominator to 0. And solve this equation in the search x.
  • If the function is square root, then the root expression cannot be negative. The subzero expression is greater or equal to 0. The result is an inequality. We solve it. We determine the intervals in which x corresponds to the equation in the positive domain or will be 0.

Third Step.

We have found out where x is or what x cannot be. Write the answer.

  • If we have a function of type inverse proportionality – the answer x will have all the values except those found as a result of solving the equation.
  • If we have a square root function, then in the answer we will write the gaps that were found as a result of the 2nd step.

If the material is not quite clear to the student, the best choice is to work it with a tutor.


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