Answer :
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)
