### Identifying Functions from Relations In this educational content, we explore how to determine whether a given relation qualifies as a function. Each relation is presented in a table or set notation, and you are tasked with identifying its function status. #### Relation 1 - **Domain and Range Table:** - Row 1: Domain = `e`, Range = `a` - Row 2: Domain = `t`, Range = `a` - Row 3: Domain = `a`, Range = `h` - Row 4: Domain = `d`, Range = `h` **Select one:** - ⭕ Function - ⭕ Not a function #### Relation 2 - **Domain and Range Table:** - Row 1: Domain = `1`, Range = `tree` - Row 2: Domain = `7`, Range = `sun` - Row 3: Domain = `3`, Range = `desk` - Row 4: Domain = `8`, Range = `moon` - Row 5: Domain = `5`, Range = `chair` **Select one:** - ⭕ Function - ⭕ Not a function #### Relation 3 - **Set of Ordered Pairs:** - \{(0, 2), (0, 1), (0, 0), (0, 6)\} **Select one:** - ⭕ Function - ⭕ Not a function #### Relation 4 - **Set of Ordered Pairs:** - \{(u, 6), (z, -7), (h, -1), (x, 2)\} **Select one:** - ⭕ Function - ⭕ Not a function After reviewing each relation, decide whether or not it is classified as a function based on the criteria that each input (domain) should map to exactly one output (range).
### Identifying Functions from Relations In this educational content, we explore how to determine whether a given relation qualifies as a function. Each relation is presented in a table or set notation, and you are tasked with identifying its function status. #### Relation 1 - **Domain and Range Table:** - Row 1: Domain = `e`, Range = `a` - Row 2: Domain = `t`, Range = `a` - Row 3: Domain = `a`, Range = `h` - Row 4: Domain = `d`, Range = `h` **Select one:** - ⭕ Function - ⭕ Not a function #### Relation 2 - **Domain and Range Table:** - Row 1: Domain = `1`, Range = `tree` - Row 2: Domain = `7`, Range = `sun` - Row 3: Domain = `3`, Range = `desk` - Row 4: Domain = `8`, Range = `moon` - Row 5: Domain = `5`, Range = `chair` **Select one:** - ⭕ Function - ⭕ Not a function #### Relation 3 - **Set of Ordered Pairs:** - \{(0, 2), (0, 1), (0, 0), (0, 6)\} **Select one:** - ⭕ Function - ⭕ Not a function #### Relation 4 - **Set of Ordered Pairs:** - \{(u, 6), (z, -7), (h, -1), (x, 2)\} **Select one:** - ⭕ Function - ⭕ Not a function After reviewing each relation, decide whether or not it is classified as a function based on the criteria that each input (domain) should map to exactly one output (range).
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Transcribed Image Text:### Identifying Functions from Relations
In this educational content, we explore how to determine whether a given relation qualifies as a function. Each relation is presented in a table or set notation, and you are tasked with identifying its function status.
#### Relation 1
- **Domain and Range Table:**
- Row 1: Domain = `e`, Range = `a`
- Row 2: Domain = `t`, Range = `a`
- Row 3: Domain = `a`, Range = `h`
- Row 4: Domain = `d`, Range = `h`
**Select one:**
- ⭕ Function
- ⭕ Not a function
#### Relation 2
- **Domain and Range Table:**
- Row 1: Domain = `1`, Range = `tree`
- Row 2: Domain = `7`, Range = `sun`
- Row 3: Domain = `3`, Range = `desk`
- Row 4: Domain = `8`, Range = `moon`
- Row 5: Domain = `5`, Range = `chair`
**Select one:**
- ⭕ Function
- ⭕ Not a function
#### Relation 3
- **Set of Ordered Pairs:**
- \{(0, 2), (0, 1), (0, 0), (0, 6)\}
**Select one:**
- ⭕ Function
- ⭕ Not a function
#### Relation 4
- **Set of Ordered Pairs:**
- \{(u, 6), (z, -7), (h, -1), (x, 2)\}
**Select one:**
- ⭕ Function
- ⭕ Not a function
After reviewing each relation, decide whether or not it is classified as a function based on the criteria that each input (domain) should map to exactly one output (range).
Expert Solution
Step 1
A function is a relation for which each value from the set of domain is associated with exactly one value from the set of range.
In our case
In relation 1
every value of domain is associated with exactly one value of range.
So
Relation 1 is a function.
In Relation 2
Clearly in relation 2 every value of domain is associated with exactly one value of range.
So
Relation 2 is a function.
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