Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Discover solutions to your questions from experienced professionals across multiple fields on our comprehensive Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
To determine which of the given options represents a function, we need to recall the definition of a function in mathematics. A function is a relation in which each element of the domain (set of inputs) is associated with exactly one element of the range (set of outputs).
Let's analyze each option:
Option A:
Since the details for Option A are not provided, we will move on to Option B and assume Option A is not the correct answer.
Option B:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline x & 5 & -5 & 10 & 5 & -10 \\ \hline y & 13 & -7 & 23 & 17 & -17 \\ \hline \end{array} \][/tex]
In Option B, observe that the domain consists of the numbers [tex]\[5, -5, 10, 5, -10\][/tex]. Here, the number 5 appears twice as an input (with outputs 13 and 17). This violates the rule of a function, as each input must map to exactly one output. Therefore, Option B does not represent a function.
Option C:
[tex]\[ \{(-7,-9),(-4,-9),(5,15),(7,19)\} \][/tex]
In Option C, each input value is unique:
- -7 maps to -9
- -4 maps to -9
- 5 maps to 15
- 7 maps to 19
No input value is repeated; each input has exactly one output, satisfying the definition of a function. Therefore, Option C represents a function.
Option D:
Since the details for Option D are not provided, we will not consider it and assume it is not the correct answer.
Based on this analysis, Option C is the correct answer as it represents a function. Thus, the answer is:
3 (representing Option C)
Let's analyze each option:
Option A:
Since the details for Option A are not provided, we will move on to Option B and assume Option A is not the correct answer.
Option B:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline x & 5 & -5 & 10 & 5 & -10 \\ \hline y & 13 & -7 & 23 & 17 & -17 \\ \hline \end{array} \][/tex]
In Option B, observe that the domain consists of the numbers [tex]\[5, -5, 10, 5, -10\][/tex]. Here, the number 5 appears twice as an input (with outputs 13 and 17). This violates the rule of a function, as each input must map to exactly one output. Therefore, Option B does not represent a function.
Option C:
[tex]\[ \{(-7,-9),(-4,-9),(5,15),(7,19)\} \][/tex]
In Option C, each input value is unique:
- -7 maps to -9
- -4 maps to -9
- 5 maps to 15
- 7 maps to 19
No input value is repeated; each input has exactly one output, satisfying the definition of a function. Therefore, Option C represents a function.
Option D:
Since the details for Option D are not provided, we will not consider it and assume it is not the correct answer.
Based on this analysis, Option C is the correct answer as it represents a function. Thus, the answer is:
3 (representing Option C)
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.