A series of points in the form (x, y) is a function if every

Question

-value is different.

A graph is a function if a vertical line passes through the graph at most
time.

Answer 1

Your statements are close but need a bit of clarification.

1. A series of points in the form \((x, y)\) represents a function if every x-value (not y-value) is associated with exactly one y-value. This means that for any given input \(x\), there should be one and only one output \(y\). If an \(x\) value corresponds to multiple \(y\) values, then it does not define a function.

2. A graph represents a function if a vertical line drawn through the graph intersects it at most once (not time). This is known as the vertical line test. If a vertical line intersects the graph at more than one point, then the graph does not represent a function.

In summary:

• A relation is a function if each \(x\) value corresponds to exactly one \(y\) value.
• A graph is a function if no vertical line intersects it at more than one point.