Question

removing which ordered pair from the table would make the relation a function of \\(x\\)?

\\(\

$$\begin{array}{|c|c|}\\hline x & y \\\\\\hline 1 & 7 \\\\\\hline 4 & 7 \\\\\\hline 2 & 2 \\\\\\hline 4 & 1 \\\\\\hline 3 & 9 \\\\\\hline\\end{array}$$

\\)

(1, 7)
(2, 2)
(3, 9)
(4, 1)

Explanation:

Identify the given relation

Using the Function Definition knowledge point

$$ R = \{(1, 7), (4, 7), (2, 2), (4, 1), (3, 9)\} $$

Analyze the definition of a function

Using the Function Definition knowledge point

$$ \forall x \in \text{Domain}, \text{ there exists exactly one } y \in \text{Codomain such that } (x, y) \in R. $$

Find the repeating input values

Using the Function Definition knowledge point

$$
LATEXBLOCK0
$$

Determine which ordered pair to remove

Using the Function Definition knowledge point

$$ \text{Remove } (4, 1) \implies \text{Remaining } x = 4 \text{ maps only to } y = 7. $$

Answer:

• (A) (1, 7)
• (B) (2, 2)
• (C) (3, 9)
• (D) (4, 1) (Correct answer)