![]() ![]() In textbooks, you will find the set of domain represented by the letter X while the set of range represented by the letter Y. Figure 1 Representation of Range as an “Image” of Domain In simple words, a function maps the set of Domain into the set of Range. RangeĪ function outputs a set of objects or numbers based on the input numbers or objects (from the set of domain). ![]() Also comment whether this relation represents a function or not. Therefore, we can say that the domain of this relation (a function actually. The first number in each of the ordered pairs represent the input whereas the second number represents the output. It is also possible that a function is conveyed in the form of a set of ordered pairs of numbers. This relation can be defined in several possible ways (equation is one of the possible ways of representation!). It should also be noted that the form in which the domain is represented here with the definition of the piecewise function is the Inequality form.Įxercise: Express the domain of the following piecewise functions in the Set-builder notation and the Interval notation.ĭomain of function in form of a Set of ordered pairsĪs you may recall that a function maps input values to output values. The domain of the following piecewise function, In other words, the set of all positive real numbers including 0. Thus, the domain of this piecewise function is i.e., the set of real numbers. Therefore, the domain of this function is the union of the set of negative real numbers and set of positive real numbers (including zero). For example, for the piecewise functionīut how to deal with two separate intervals? It is surprisingly easy. The domain of a piecewise function is mentioned in its expression. The second method will be discussed later when we will look at the graph of a function. Notice that you will always find the infinity symbol with a round bracket. Therefore, the domain of the function turns out to be [4,∞) i.e., the function is defined for x equal to and greater than 4. For example, if, then it can be noticed that the expression (x – 4) becomes negative for x < 4. If a square root appears, then you have to make sure that the inside of it does not become negative. It is also possible that the function includes square root. Thus, the domain of the function becomes the set of real numbers excluding the numbers -1 and 5. For example, if, you should immediately realize that the denominator becomes 0 at x = -1 and x = 5 and nowhere else. If that is the case, the domain of the function will exclude all those values of x for which the denominator equates to 0. An easy way to do that is to see if there is any fraction in the expression where the independent variable x lies in the denominator. Once you find that, you just have to exclude that region of input values. ![]() If you are given the expression of a function, then you should try to find where function is not defined. Two methods will be discussed in this article. For example, the domain of the function is represented in interval notation asĮxercise: Find the domain of the function and represent it using all of the three notations discussed above. If zero were included, we would have used the square bracket. The round bracket with 0 represents that 0 is not included. Taking the example of the function yet again, the domain can be represented in interval notation as Similarly, the function cannot output a real number for x symbols, whereas square brackets are used to replace the ≤, ≥ symbols. For example, the function is undefined when you plug in the number x = 0. You should realize that some functions ‘ break’ at some input values (or in other words, the rule that a function is based on cannot be applied to some numbers). A function has to be passed some numbers as the values of the independent variable x. You may recall that a function is represented in form of an expression that involves the use of an independent variable (usually represented with the symbol x). Here we will discuss about those numbers (input and output), what they are called, their notation etc. In textbooks, a function is usually attributed as a mathematical machine that swallows a number, processes it (based on some rule) and spits out another number. The operation can as simple as multiplying the input with 1 (basically doing nothing). A function basically takes some values and outputs corresponding values after performing some operation on it. You may recall what a function is and what it does. ![]()
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