Question

which statement best describes the relationship shown in the equation?
y = x²
a. this is a functional relationship.
b. it cannot be determined if this is or is not a functional relationship.
c. this is not a functional relationship.

Explanation:

To determine if \( y = x^2 \) is a function, we use the vertical line test (for graphs) or the definition: a relation is a function if each input (\( x \)) has exactly one output (\( y \)). For any \( x \)-value, squaring it gives exactly one \( y \)-value (e.g., \( x = 2 \) gives \( y = 4 \), \( x=-2 \) gives \( y = 4 \); each \( x \) has one \( y \), even if multiple \( x \) share a \( y \)). Thus, \( y = x^2 \) is a functional relationship.

Answer:

A. This is a functional relationship.