How Indentify The Relation Is Function

If a relation is a function, it has to satisfy the following conditions. i Domain of f is A. ii For each x A, there is only one y B such that x, y f. Let us look at some examples to understand how to determine whether a relation is a function or not. Example 1 Does the following relation represent a function ? Explain.

A function is a relation in which each element of the domain is paired with exactly one element in the range. Looking at the mapping diagram above, the elements in the domain are -5, 1, 6, 0 and the elements in the range are 9, -2, -6, 10 Since 1 is paired with two elements in the range 9 and -6 , the relation is not a function.

If all the input values are different, then the relation becomes a function, and if the values are repeated, the relation is not a function. Note if there is a repetition of the first members with an associated repetition of the second members, the relation becomes a function. Example 1. Identify the range and domain the relation below -2

If the vertical line hits two or more points at the same X location, the relation is not a function. In other words, if two or more points have the same X value and different Y values, the relation is not a function. The relation is a function if you move the vertical line across the graph without hitting two or more points at the same time.

How To Given a relationship between two quantities, determine whether the relationship is a function. Identify the input values. Identify the output values. If each input value leads to only one output value, classify the relationship as a function. If any input value leads to two or more outputs, do not classify the relationship as a function.

Let's go over a few more examples by identifying if a given relation is a function or not. Example 1 Is the relation expressed in the mapping diagram a function? Each element of the domain is being traced to one and only element in the range. However, it is okay for two or more values in the domain to share a common value in the range.

When a change in value of one variable causes a change in the value of another variable, their interaction is called a relation. A relation has an input value which corresponds to an output value. When each input value has one and only one output value, that relation is a function. Functions can be written as ordered pairs, tables, or graphs.

Relations. Determine if the Relation is a Function, Step 1. Since there is one value of for every value of in , this relation is a function. The relation is a function. Enter YOUR Problem. About Examples Glossary Affiliates Advertise with us Careers

Mathematical Representation. Mathematicians usually represent functions by the letters quot f x ,quot although any other letters work just as well.You read the letters as quot f of x .quotIf you choose to represent the function as g y , you would read it as quot g of y .quotThe equation for the function defines the rule by which the input value x is transformed into another number.

Since relation 1 has ONLY ONE y value for each x value, this relation is a function. On the other hand, relation 2 has TWO distinct y values 'a' and 'c' for the same x value of '5' . Therefore, relation 2 does not satisfy the definition of a mathematical function.