Question

1. which of the following graphs represents a function?

a. a straight diagonal line
b. a graph with one input and multiple outputs
c. a graph of a circle
d. a vertical line

Explanation:

A relation is a function if every input (x-value) has exactly one output (y-value), which is verified by the Vertical Line Test: any vertical line drawn on the graph intersects it at most once.

• A straight diagonal line (non-vertical) passes the Vertical Line Test, as each x maps to one y.
• A graph with one input and multiple outputs fails, since one x has multiple y-values.
• A circle fails the Vertical Line Test, as vertical lines intersect it twice.
• A vertical line fails, as one x has infinitely many y-values.

Answer:

a. A straight diagonal line