Question

module 2.2 quiz
the set of ordered pairs shows a relationship between x and y.
{(-3, 2), (-2, 2), (2, -3), (3, -2)}
which statement is true for the set of ordered pairs?
a y is not a function of x, since there are more x-values than different corresponding y-values.
b y is a function of x, since the y-values do correspond to exactly one x-value.
c y is not a function of x, since the x-values do not correspond to exactly one y-value.
d y is a function of x, since the x-values do correspond to exactly one y-value.

Explanation:

Step1: Recall Function Definition

A function is a relation where each \( x \)-value (input) has exactly one \( y \)-value (output).

Step2: Analyze Given Ordered Pairs

The ordered pairs are \((-3, 2)\), \((-2, 2)\), \((2, -3)\), \((3, -2)\). Check each \( x \)-value:

• \( x = -3 \) maps to \( y = 2 \)
• \( x = -2 \) maps to \( y = 2 \)
• \( x = 2 \) maps to \( y = -3 \)
• \( x = 3 \) maps to \( y = -2 \)

Each \( x \)-value has exactly one \( y \)-value.

Step3: Evaluate Options

• Option A: Incorrect, as \( x \)-values have unique \( y \)-values (function).
• Option B: Incorrect, function is \( x \to y \), not \( y \to x \).
• Option C: Incorrect, \( x \)-values do correspond to exactly one \( y \)-value.
• Option D: Correct, since each \( x \)-value has exactly one \( y \)-value.

Answer:

D. \( y \) is a function of \( x \), since the \( x \)-values do correspond to exactly one \( y \)-value.