The vertical line test is a graphical method used to determine whether a curve represents a function. It involves drawing vertical lines (lines parallel to the y-axis) through the graph of a relation and observing the number of intersection points between the vertical line and the graph. How the Vertical Line Test Works:

• For a graph to represent a function, each input value (x-value) must correspond to exactly one output value (y-value).
• When you draw a vertical line at any x-value, it should intersect the graph at only one point.
• If any vertical line intersects the graph more than once, that means a single x-value corresponds to multiple y-values, so the graph does not represent a function.

Summary:

• If every vertical line crosses the graph at exactly one point, the graph is a function.
• If any vertical line crosses the graph at more than one point, the graph is not a function.

Example:

• The graph of y=x+1y=x+1y=x+1 passes the vertical line test because any vertical line intersects it once.
• The graph of a circle, such as x2+y2=9x^2+y^2=9x2+y2=9, fails the test because some vertical lines intersect it twice.

The vertical line test visually confirms the fundamental definition of a function: each input has a unique output