Connect with knowledgeable individuals and get your questions answered on IDNLearn.com. Our platform provides detailed and accurate responses from experts, helping you navigate any topic with confidence.
Sagot :
To determine which relation represents a function, we need to recall the definition of a function. A relation is a function if each input (or [tex]\( x \)[/tex]-value) is associated with exactly one output (or [tex]\( y \)[/tex]-value). In other words, no [tex]\( x \)[/tex]-value should be associated with more than one [tex]\( y \)[/tex]-value.
Let's analyze each given relation:
1. Relation 1: [tex]\(\{(0,0),(2,3),(2,5),(6,6)\}\)[/tex]
- For [tex]\( x = 0 \)[/tex], the corresponding [tex]\( y \)[/tex]-value is [tex]\( 0 \)[/tex].
- For [tex]\( x = 2 \)[/tex], there are two corresponding [tex]\( y \)[/tex]-values: [tex]\( 3 \)[/tex] and [tex]\( 5 \)[/tex].
Since the [tex]\( x \)[/tex]-value [tex]\( 2 \)[/tex] is associated with more than one [tex]\( y \)[/tex]-value, this relation does not represent a function.
2. Relation 2: [tex]\(\{(3,5),(8,4),(10,11),(10,8)\}\)[/tex]
- For [tex]\( x = 3 \)[/tex], the corresponding [tex]\( y \)[/tex]-value is [tex]\( 5 \)[/tex].
- For [tex]\( x = 8 \)[/tex], the corresponding [tex]\( y \)[/tex]-value is [tex]\( 4 \)[/tex].
- For [tex]\( x = 10 \)[/tex], there are two corresponding [tex]\( y \)[/tex]-values: [tex]\( 11 \)[/tex] and [tex]\( 8 \)[/tex].
Since the [tex]\( x \)[/tex]-value [tex]\( 10 \)[/tex] is associated with more than one [tex]\( y \)[/tex]-value, this relation does not represent a function.
3. Relation 3: [tex]\(\{(-2,2),(0,2),(-2,1),(2,2)\}\)[/tex]
- For [tex]\( x = -2 \)[/tex], there are two corresponding [tex]\( y \)[/tex]-values: [tex]\( 2 \)[/tex] and [tex]\( 1 \)[/tex].
- For [tex]\( x = 0 \)[/tex], the corresponding [tex]\( y \)[/tex]-value is [tex]\( 2 \)[/tex].
- For [tex]\( x = 2 \)[/tex], the corresponding [tex]\( y \)[/tex]-value is [tex]\( 2 \)[/tex].
Since the [tex]\( x \)[/tex]-value [tex]\( -2 \)[/tex] is associated with more than one [tex]\( y \)[/tex]-value, this relation does not represent a function.
4. Relation 4: [tex]\(\{(13,2),(13,3),(13,4),(13,5)\}\)[/tex]
- For [tex]\( x = 13 \)[/tex], there are four corresponding [tex]\( y \)[/tex]-values: [tex]\( 2 \)[/tex], [tex]\( 3 \)[/tex], [tex]\( 4 \)[/tex], and [tex]\( 5 \)[/tex].
Since the [tex]\( x \)[/tex]-value [tex]\( 13 \)[/tex] is associated with more than one [tex]\( y \)[/tex]-value, this relation does not represent a function.
According to our analysis, none of the given relations represent a function. Therefore, there is no relation among the four provided that can be considered a function.
Let's analyze each given relation:
1. Relation 1: [tex]\(\{(0,0),(2,3),(2,5),(6,6)\}\)[/tex]
- For [tex]\( x = 0 \)[/tex], the corresponding [tex]\( y \)[/tex]-value is [tex]\( 0 \)[/tex].
- For [tex]\( x = 2 \)[/tex], there are two corresponding [tex]\( y \)[/tex]-values: [tex]\( 3 \)[/tex] and [tex]\( 5 \)[/tex].
Since the [tex]\( x \)[/tex]-value [tex]\( 2 \)[/tex] is associated with more than one [tex]\( y \)[/tex]-value, this relation does not represent a function.
2. Relation 2: [tex]\(\{(3,5),(8,4),(10,11),(10,8)\}\)[/tex]
- For [tex]\( x = 3 \)[/tex], the corresponding [tex]\( y \)[/tex]-value is [tex]\( 5 \)[/tex].
- For [tex]\( x = 8 \)[/tex], the corresponding [tex]\( y \)[/tex]-value is [tex]\( 4 \)[/tex].
- For [tex]\( x = 10 \)[/tex], there are two corresponding [tex]\( y \)[/tex]-values: [tex]\( 11 \)[/tex] and [tex]\( 8 \)[/tex].
Since the [tex]\( x \)[/tex]-value [tex]\( 10 \)[/tex] is associated with more than one [tex]\( y \)[/tex]-value, this relation does not represent a function.
3. Relation 3: [tex]\(\{(-2,2),(0,2),(-2,1),(2,2)\}\)[/tex]
- For [tex]\( x = -2 \)[/tex], there are two corresponding [tex]\( y \)[/tex]-values: [tex]\( 2 \)[/tex] and [tex]\( 1 \)[/tex].
- For [tex]\( x = 0 \)[/tex], the corresponding [tex]\( y \)[/tex]-value is [tex]\( 2 \)[/tex].
- For [tex]\( x = 2 \)[/tex], the corresponding [tex]\( y \)[/tex]-value is [tex]\( 2 \)[/tex].
Since the [tex]\( x \)[/tex]-value [tex]\( -2 \)[/tex] is associated with more than one [tex]\( y \)[/tex]-value, this relation does not represent a function.
4. Relation 4: [tex]\(\{(13,2),(13,3),(13,4),(13,5)\}\)[/tex]
- For [tex]\( x = 13 \)[/tex], there are four corresponding [tex]\( y \)[/tex]-values: [tex]\( 2 \)[/tex], [tex]\( 3 \)[/tex], [tex]\( 4 \)[/tex], and [tex]\( 5 \)[/tex].
Since the [tex]\( x \)[/tex]-value [tex]\( 13 \)[/tex] is associated with more than one [tex]\( y \)[/tex]-value, this relation does not represent a function.
According to our analysis, none of the given relations represent a function. Therefore, there is no relation among the four provided that can be considered a function.
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Find precise solutions at IDNLearn.com. Thank you for trusting us with your queries, and we hope to see you again.
