Questions: State the domain and range for the following relation. Then determine whether the relation represents a function. Choose the correct answer below. Domain : Head, Legs, Torso, Feet Range : Hat, Ear muffs, Skirt, Shirt, Shoes Domain : Head, Torso, Feet, Hat, Shirt, Shoes Range : Legs, Ear muffs, Skirt Domain : Legs, Ear muffs, Skirt Range : Head, Torso, Feet, Hat, Shirt, Shoes Domain : Hat, Ear muffs, Skirt, Shirt, Shoes Range : Head, Legs, Torso, Feet Does the relation represent a function? A. The relation in the figure is not a function because the element Hat in the range corresponds to more than one element in the domain. B. The relation in the figure is a function because each element in the domain corresponds to exactly one element in the range. C. The relation in the figure is a function because each element in the range corresponds to exactly one element in the domain. D. The relation in the figure is not a function because the element Head in the domain corresponds to more than one element in the range.

State the domain and range for the following relation. Then determine whether the relation represents a function. Choose the correct answer below. Domain : Head, Legs, Torso, Feet Range : Hat, Ear muffs, Skirt, Shirt, Shoes Domain : Head, Torso, Feet, Hat, Shirt, Shoes Range : Legs, Ear muffs, Skirt Domain : Legs, Ear muffs, Skirt Range : Head, Torso, Feet, Hat, Shirt, Shoes Domain : Hat, Ear muffs, Skirt, Shirt, Shoes Range : Head, Legs, Torso, Feet Does the relation represent a function? A. The relation in the figure is not a function because the element Hat in the range corresponds to more than one element in the domain. B. The relation in the figure is a function because each element in the domain corresponds to exactly one element in the range. C. The relation in the figure is a function because each element in the range corresponds to exactly one element in the domain. D. The relation in the figure is not a function because the element Head in the domain corresponds to more than one element in the range.
Transcript text: State the domain and range for the following relation. Then determine whether the relation represents a function. Choose the correct answer below. Domain : {Head, Legs, Torso, Feet} Range : {Hat, Ear muffs, Skirt, Shirt, Shoes} Domain : {Head, Torso, Feet, Hat, Shirt, Shoes} Range : {Legs, Ear muffs, Skirt} Domain : {Legs, Ear muffs, Skirt} Range : {Head, Torso, Feet, Hat, Shirt, Shoes} Domain : {Hat, Ear muffs, Skirt, Shirt, Shoes} Range : {Head, Legs, Torso, Feet} Does the relation represent a function? A. The relation in the figure is not a function because the element Hat in the range corresponds to more than one element in the domain. B. The relation in the figure is a function because each element in the domain corresponds to exactly one element in the range. C. The relation in the figure is a function because each element in the range corresponds to exactly one element in the domain. D. The relation in the figure is not a function because the element Head in the domain corresponds to more than one element in the range.
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Solution

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Solution Steps

Step 1: Find the domain

The domain is the set of all inputs of a relation. In this case, the body parts are the inputs. Thus, the domain is {Head, Legs, Torso, Feet}.

Step 2: Find the range

The range is the set of all outputs of a relation. Here, the clothing items are the outputs. Thus, the range is {Hat, Ear muffs, Skirt, Shirt, Shoes}.

Step 3: Determine if the relation is a function

A relation is a function if each input corresponds to exactly one output. In the given relation, each body part corresponds to exactly one clothing item. The Head corresponds to a Hat, Legs correspond to Ear muffs and Shoes, the Torso corresponds to a Shirt, and Feet correspond to Shoes. Since the Legs and Feet correspond to Shoes, Head corresponds to Hat and Legs corresponds to Ear muffs, the "Head" and "Legs" each have two outputs. Therefore, the relation is not a function.

Final Answer:

Domain: {Head, Legs, Torso, Feet} Range: {Hat, Ear muffs, Skirt, Shirt, Shoes} The relation is not a function because the elements Head and Legs in the domain correspond to more than one element in the range. Specifically, Head corresponds to Hat and Earmuffs. Legs corresponds to Shoes and Earmuffs. Also Feet corresponds to Shoes.

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