Identify the mapping diagram that represents the given relation and determine whether the relation is a function. {(–3, –6), (–1, –6), (5, –6), (8, –6)}

Identify the mapping diagram that represents the given relation and determine whether the relation is a function. {(–8, –6), (–5, 2), (–8,1), (7, 3)}

#1) This is a function.
#2) This is not a function.
(The mapping diagrams are not present to match to these.)

Explanation:
A function is a relation in which each element of the domain is matched to no more than one element of the range; in other words, no x gets mapped to more than 1 y.

In #1, no x is mapped to more than 1 y, so it is a function. However, in #2, -8 is mapped to both -6 and to 1; this x is used more than once, so this is not a function.

danielmaduroh danielmaduroh · Answer 2 · 2018-08-02T22:52:33-04:00

Recall that a function \(f\) from a set \(A\) to a set \(B\) is a relation that assigns to each element \(x\) in the set \(A\) exactly one element in the set \(B\). The set \(A\) is the domain (or set of inputs) of the function and the set \(B\) contains the range (or set of outputs).

The general characteristics of functions are:

a. Each element in A must be matched with an element in B.

b. Some elements in B may not be matched with any element in A.

c. Two or more elements in A may be matched with the same element in B.

d. An element in A (the domain) can not be matched with two different elements in B.

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Solving this problem we have:

1. The mapping diagram is represented in Figure 1. As you can see this is a function. Each element in A is matched with an element in B. All the elements in A are matched with the same element in B. So, this fulfills with the definition of function.

2. The mapping diagram is represented in Figure 2. This is not a function. Notice that an element in A (the domain) is matched with two different elements in B, that is, -8 is matched with -6 and 1.