Question

which ordered pair
$(x,y)$ makes the relation a function?
${(3, 4), (-2, 6), (5, 5), (-4, 6), (x, y)}$
a. $(-4, 4)$

b. $(-2, 5)$

c. $(0, 6)$

d. $(3, 6)$

Explanation:

Step1: Recall function definition

A relation is a function if each input ($x$-value) has exactly one output ($y$-value). So we need an $(x,y)$ where $x$ is not already in the given set.

Step2: List existing $x$-values

Existing $x$-values: $3, -2, 5, -4$

Step3: Check each option

• Option A: $x=-4$ (already exists)
• Option B: $x=-2$ (already exists)
• Option C: $x=0$ (not in existing set)
• Option D: $x=3$ (already exists)

Answer:

C. (0, 6)