Question

1. 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)}
2. 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)}

Answer 1

#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.

Answer 2

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.