Math Problem Statement
Solution
Let's analyze the problem in the image.
Problem:
The problem asks to:
- Identify the correct domain and range for a given relation.
- Determine whether the relation represents a function.
First, the domain and range:
The provided diagram illustrates a relation between two sets:
- Set 1 (Domain): It contains plant types such as "Shrub", "Daisy", and "Herb".
- Set 2 (Range): It contains names of plants such as "Basil", "Rose", "Oak", and "Flower".
Mapping:
The arrows in the diagram indicate the relationship between elements of the domain and range:
- Shrub maps to Basil.
- Shrub also maps to Rose.
- Daisy maps to Flower.
- Herb maps to Oak.
- Tree maps to Oak.
Analyzing the domain and range:
- Domain: The elements that are being mapped from: Shrub, Daisy, Herb, Tree.
- Range: The elements that are being mapped to: Basil, Rose, Flower, Oak.
So, the correct domain is: .
The correct range is: .
Determining whether this is a function:
A relation is a function if every element in the domain is mapped to exactly one element in the range.
- Shrub is mapped to both Basil and Rose, which means one element in the domain is mapped to more than one element in the range.
Thus, this relation is not a function.
Conclusion:
The correct answer would be:
- Domain:
- Range:
- The relation does not represent a function because an element in the first set (Shrub) corresponds to more than one element in the second set.
This corresponds to the following options in the image:
- Domain: Shrub, Daisy, Herb, Tree.
- Range: Basil, Rose, Flower, Oak.
- Option B: "No, because each element in the first set corresponds to exactly one element in the second set."
Would you like more details on how relations and functions work?
Here are 5 related questions to expand on this:
- What are the differences between a relation and a function?
- How can you determine if a relation is a function from its graph?
- What are examples of real-world functions?
- Can a function have multiple outputs for a single input?
- How do you represent functions using set notation?
Tip: A function assigns exactly one output to each input. If any input has more than one output, the relation is not a function.
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Math Problem Analysis
Mathematical Concepts
Relations
Functions
Set Theory
Formulas
-
Theorems
Definition of Function
Set and Relations Theory
Suitable Grade Level
Grades 7-9