A function is relation that maps a set of elements known as inputs to another set of elements known as the outputs, such that each input element is mapped to exactly one output element
The relationship between the given values is a function and, the correct option is; Yes, there is no value in the domain that corresponds to more than one value of the range
The reasons the selected option are correct is as follows:
The given ordered pair are presented in a tabular form as follows:
[tex]\begin{array}{|c|cc|}\mathbf{Domain \ (x)}&&\mathbf{Range \ (y)}\\1&&3\\-4&&0\\3&&1\\0&&4\\2&&3\end{array}\right][/tex]
In a function, each value in the domain corresponds with one element in the range. Therefore, if two elements in the domain corresponds to one element in the range, the relationship is not a function
Therefore;
[tex]\begin{array}{|c|cc|}\mathbf{ x}&&\mathbf{y}\\1&&1\\1&&2\\1&&3\\1&&4\\1&&5\end{array}\right] \ Is \ not \ a \ function[/tex]
[tex]\begin{array}{|c|cc|}\mathbf{Domain \ (x)}&&\mathbf{Range \ (y)}\\1&&3\\-4&&0\\3&&1\\0&&4\\2&&3\end{array}\right] \ Is \ a \ function[/tex]
In the table above, each element in the domain appear only once, and therefore, each element in the domain correspond or gives only one value in the range, while the element 3 in the range corresponds to 1, and 2 in the domain. However, the range are the output values of the function, and therefore, the data satisfies the relationship of a function
The correct option is; Yes, there is no value in the domain that corresponds to more than one value of the range
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