Problem

Given the table below, determine whether $y$ is a function of $x$ and if the function is one-to-one.
\begin{tabular}{c|c}
$x$ & $y$ \\
\hline 6 & -2 \\
3 & 7 \\
1 & 2 \\
4 & 8
\end{tabular}

Answer

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Answer

\(\boxed{\text{Therefore, } y \text{ is a function of } x \text{ and the function is one-to-one.}}\)

Steps

Step 1 :To determine whether \(y\) is a function of \(x\), we need to check if each \(x\) value has exactly one corresponding \(y\) value. Looking at the table, we can see that each \(x\) value is unique and has exactly one corresponding \(y\) value. Therefore, \(y\) is a function of \(x\).

Step 2 :To determine whether the function is one-to-one, we need to check if each \(y\) value has exactly one corresponding \(x\) value. Looking at the table, we can see that each \(y\) value is unique and has exactly one corresponding \(x\) value. Therefore, the function is one-to-one.

Step 3 :\(\boxed{\text{Therefore, } y \text{ is a function of } x \text{ and the function is one-to-one.}}\)

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