the x values and their output form a function
Explanation:[tex]\begin{gathered} x\text{ = }\mleft\lbrace-1,\text{ 0, 3, 8, 15}\mright\rbrace \\ \text{The relation machine:} \\ y\text{ = }\sqrt[]{x+1} \end{gathered}[/tex][tex]\begin{gathered} \text{when x = -1} \\ y\text{ = }\sqrt[]{-1+1}\text{ = }\sqrt[]{0}\text{ = 0} \\ \text{when x = 0} \\ y\text{ = }\sqrt[]{0+1}\text{ = }\sqrt[]{1}\text{ = 1} \\ \text{when x = 3} \\ y\text{ = }\sqrt[]{3+1}\text{ = }\sqrt[]{4}\text{ = 2} \\ \text{when x = 8} \\ y\text{ = }\sqrt[]{8+1}\text{ = }\sqrt[]{9}\text{ = 3} \\ \text{when x = 15} \\ y\text{ = }\sqrt[]{15+1}\text{ = }\sqrt[]{16}\text{ = 4} \end{gathered}[/tex]For the relation to be a function, each of the input will have only one output.
From the solution for the values of y, each of the x values have one y value
Hence, the x values and their output form a function