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

Which of the following is true?

choice b.

choice c.

choice d.

choice a.

Determine if the relation is a function.

The relation is a function.

Find the domain and range.

Domain:

{ − 3 , − 1 ,  5 ,  8 }

Range:

{ − 6 }

Graph.

{ ( − 3 , − 6 ) ,   ( − 1 ,  − 6 ) ,   ( 5 ,  − 6 ) ,   ( 8 ,  − 6 ) }

Step-by-step explanation:

1:    Recall that a function  from a set  to a set  is a relation that assigns to each element  in the set  exactly one element in the set . The set  is the domain (or set of inputs) of the function and the set  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.

2:    #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.

54

step-by-step explanation:

6x9

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1