IDNLearn.com: Where your questions meet expert advice and community insights. Explore a wide array of topics and find reliable answers from our experienced community members.
Sagot :
Sure, let's analyze both the table of values and the given points to determine whether each represents a function.
### Analyzing the Table of Values:
To determine if a table represents a function, we need to ensure that each input value ([tex]\(x\)[/tex]) maps to exactly one output value ([tex]\(y\)[/tex]). In other words, no [tex]\(x\)[/tex] value should repeat with different [tex]\(y\)[/tex] values.
#### Table:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline -10 & 84 \\ \hline -5 & 31.5 \\ \hline 0 & 4 \\ \hline 5 & 1.5 \\ \hline 10 & 24 \\ \hline \end{array} \][/tex]
We will examine the [tex]\(x\)[/tex] values here to see if any of them repeat:
- [tex]\(x = -10\)[/tex]
- [tex]\(x = -5\)[/tex]
- [tex]\(x = 0\)[/tex]
- [tex]\(x = 5\)[/tex]
- [tex]\(x = 10\)[/tex]
Since each [tex]\(x\)[/tex] value appears only once, the table does indeed represent a function.
### Analyzing the List of Points:
Similar to the table analysis, for the list of points to represent a function, each [tex]\(x\)[/tex] value should map to exactly one [tex]\(y\)[/tex] value.
#### Points:
[tex]\[ (4, 5), (6, -2), (-5, 0), (6, 1) \][/tex]
We will examine the [tex]\(x\)[/tex] values here to see if any of them repeat:
- [tex]\(x = 4\)[/tex]
- [tex]\(x = 6\)[/tex]
- [tex]\(x = -5\)[/tex]
- [tex]\(x = 6\)[/tex]
We can see that [tex]\(x = 6\)[/tex] appears twice with different [tex]\(y\)[/tex] values ([tex]\(-2\)[/tex] and [tex]\(1\)[/tex]). This means that the list of points does not represent a function.
### Conclusion:
From the analysis:
- The table of values represents a function because there are no duplicate [tex]\(x\)[/tex] values.
- The list of points does not represent a function because there is a duplicate [tex]\(x\)[/tex] value ([tex]\(x = 6\)[/tex]) with different [tex]\(y\)[/tex] values.
Therefore, the correct answer to the question is that neither the table nor the points represent a function, since the list of points violates the condition of having unique [tex]\(x\)[/tex] values. But since we are to determine which of them represents a function, only the table holds. The final determination:
- The given points [tex]\((4, 5), (6, -2), (-5, 0), (6, 1)\)[/tex] do not form a function.
Thus, considering the most inclusive answer in summary:
- False: Neither structure strictly holds the criteria under all conditions as true representations of a strict function ensemble.
### Analyzing the Table of Values:
To determine if a table represents a function, we need to ensure that each input value ([tex]\(x\)[/tex]) maps to exactly one output value ([tex]\(y\)[/tex]). In other words, no [tex]\(x\)[/tex] value should repeat with different [tex]\(y\)[/tex] values.
#### Table:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline -10 & 84 \\ \hline -5 & 31.5 \\ \hline 0 & 4 \\ \hline 5 & 1.5 \\ \hline 10 & 24 \\ \hline \end{array} \][/tex]
We will examine the [tex]\(x\)[/tex] values here to see if any of them repeat:
- [tex]\(x = -10\)[/tex]
- [tex]\(x = -5\)[/tex]
- [tex]\(x = 0\)[/tex]
- [tex]\(x = 5\)[/tex]
- [tex]\(x = 10\)[/tex]
Since each [tex]\(x\)[/tex] value appears only once, the table does indeed represent a function.
### Analyzing the List of Points:
Similar to the table analysis, for the list of points to represent a function, each [tex]\(x\)[/tex] value should map to exactly one [tex]\(y\)[/tex] value.
#### Points:
[tex]\[ (4, 5), (6, -2), (-5, 0), (6, 1) \][/tex]
We will examine the [tex]\(x\)[/tex] values here to see if any of them repeat:
- [tex]\(x = 4\)[/tex]
- [tex]\(x = 6\)[/tex]
- [tex]\(x = -5\)[/tex]
- [tex]\(x = 6\)[/tex]
We can see that [tex]\(x = 6\)[/tex] appears twice with different [tex]\(y\)[/tex] values ([tex]\(-2\)[/tex] and [tex]\(1\)[/tex]). This means that the list of points does not represent a function.
### Conclusion:
From the analysis:
- The table of values represents a function because there are no duplicate [tex]\(x\)[/tex] values.
- The list of points does not represent a function because there is a duplicate [tex]\(x\)[/tex] value ([tex]\(x = 6\)[/tex]) with different [tex]\(y\)[/tex] values.
Therefore, the correct answer to the question is that neither the table nor the points represent a function, since the list of points violates the condition of having unique [tex]\(x\)[/tex] values. But since we are to determine which of them represents a function, only the table holds. The final determination:
- The given points [tex]\((4, 5), (6, -2), (-5, 0), (6, 1)\)[/tex] do not form a function.
Thus, considering the most inclusive answer in summary:
- False: Neither structure strictly holds the criteria under all conditions as true representations of a strict function ensemble.
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Your questions deserve accurate answers. Thank you for visiting IDNLearn.com, and see you again for more solutions.
