Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Connect with a community of experts ready to provide precise solutions to your questions on our user-friendly Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
To determine which of the given options represents a function, we need to understand the definition of a function in terms of mappings from domain to range. A set of ordered pairs represents a function if each input (or [tex]\( x \)[/tex]-value) is associated with exactly one output (or [tex]\( y \)[/tex]-value). This means that no [tex]\( x \)[/tex]-value is repeated with a different [tex]\( y \)[/tex]-value.
Let's analyze the given options:
### Option B
The set of coordinates is: [tex]\(\{(-1,-11),(0,-7),(1,-3),(-1,5),(2,0)\}\)[/tex].
To check if this set of coordinates represents a function, let's list out the [tex]\( x \)[/tex]-values:
- From [tex]\((-1,-11)\)[/tex] : [tex]\( x = -1 \)[/tex]
- From [tex]\((0,-7)\)[/tex] : [tex]\( x = 0 \)[/tex]
- From [tex]\((1,-3)\)[/tex] : [tex]\( x = 1 \)[/tex]
- From [tex]\((-1,5)\)[/tex] : [tex]\( x = -1 \)[/tex]
- From [tex]\((2,0)\)[/tex] : [tex]\( x = 2 \)[/tex]
We observe that the [tex]\( x \)[/tex]-value [tex]\(-1\)[/tex] appears twice, once with the [tex]\( y \)[/tex]-value [tex]\(-11\)[/tex] and once with the [tex]\( y \)[/tex]-value [tex]\(5\)[/tex]. This means that for [tex]\( x = -1 \)[/tex], we have two different outputs ([tex]\(-11\)[/tex] and [tex]\(5\)[/tex]), indicating that option B does not represent a function.
### Option C
The table given is:
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|} \hline x & -18 & -13 & 3 & 5 & -6 & 3 \\ \hline y & -7 & -2 & 14 & 16 & 5 & 19 \\ \hline \end{array} \][/tex]
To check if this table represents a function, let's list out the [tex]\( x \)[/tex]-values and check for duplicates:
- [tex]\(-18\)[/tex]
- [tex]\(-13\)[/tex]
- [tex]\(3\)[/tex]
- [tex]\(5\)[/tex]
- [tex]\(-6\)[/tex]
- [tex]\(3\)[/tex]
Here, we observe that the [tex]\( x \)[/tex]-value [tex]\(3\)[/tex] appears twice, once with the [tex]\( y \)[/tex]-value [tex]\(14\)[/tex] and once with the [tex]\( y \)[/tex]-value [tex]\(19\)[/tex]. This means that for [tex]\( x = 3 \)[/tex], we have two different outputs ([tex]\(14\)[/tex] and [tex]\(19\)[/tex]), indicating that option C does not represent a function.
### Conclusion
Since neither Option B nor Option C satisfies the requirement that each [tex]\( x \)[/tex]-value must map to exactly one [tex]\( y \)[/tex]-value, neither option represents a function.
Therefore, the answer is:
```
None
```
Let's analyze the given options:
### Option B
The set of coordinates is: [tex]\(\{(-1,-11),(0,-7),(1,-3),(-1,5),(2,0)\}\)[/tex].
To check if this set of coordinates represents a function, let's list out the [tex]\( x \)[/tex]-values:
- From [tex]\((-1,-11)\)[/tex] : [tex]\( x = -1 \)[/tex]
- From [tex]\((0,-7)\)[/tex] : [tex]\( x = 0 \)[/tex]
- From [tex]\((1,-3)\)[/tex] : [tex]\( x = 1 \)[/tex]
- From [tex]\((-1,5)\)[/tex] : [tex]\( x = -1 \)[/tex]
- From [tex]\((2,0)\)[/tex] : [tex]\( x = 2 \)[/tex]
We observe that the [tex]\( x \)[/tex]-value [tex]\(-1\)[/tex] appears twice, once with the [tex]\( y \)[/tex]-value [tex]\(-11\)[/tex] and once with the [tex]\( y \)[/tex]-value [tex]\(5\)[/tex]. This means that for [tex]\( x = -1 \)[/tex], we have two different outputs ([tex]\(-11\)[/tex] and [tex]\(5\)[/tex]), indicating that option B does not represent a function.
### Option C
The table given is:
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|} \hline x & -18 & -13 & 3 & 5 & -6 & 3 \\ \hline y & -7 & -2 & 14 & 16 & 5 & 19 \\ \hline \end{array} \][/tex]
To check if this table represents a function, let's list out the [tex]\( x \)[/tex]-values and check for duplicates:
- [tex]\(-18\)[/tex]
- [tex]\(-13\)[/tex]
- [tex]\(3\)[/tex]
- [tex]\(5\)[/tex]
- [tex]\(-6\)[/tex]
- [tex]\(3\)[/tex]
Here, we observe that the [tex]\( x \)[/tex]-value [tex]\(3\)[/tex] appears twice, once with the [tex]\( y \)[/tex]-value [tex]\(14\)[/tex] and once with the [tex]\( y \)[/tex]-value [tex]\(19\)[/tex]. This means that for [tex]\( x = 3 \)[/tex], we have two different outputs ([tex]\(14\)[/tex] and [tex]\(19\)[/tex]), indicating that option C does not represent a function.
### Conclusion
Since neither Option B nor Option C satisfies the requirement that each [tex]\( x \)[/tex]-value must map to exactly one [tex]\( y \)[/tex]-value, neither option represents a function.
Therefore, the answer is:
```
None
```
We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.
