Question

which graph is a relation (non - function)?

Explanation:

To determine which graph is a non - function (a relation that is not a function), we use the vertical line test. A graph represents a function if and only if no vertical line intersects the graph more than once.

Step 1: Analyze Graph A

Graph A is a straight line (linear graph). For any vertical line \(x = a\) (where \(a\) is a real number), this vertical line will intersect the linear graph at most once. So, Graph A represents a function.

Step 2: Analyze Graph B

Graph B is a parabola opening upwards. For any vertical line \(x=a\), this vertical line will intersect the parabola at most once. So, Graph B represents a function.

Step 3: Analyze Graph C

Graph C is a triangle - shaped graph. If we draw a vertical line (for example, a vertical line that passes through the middle of the horizontal side of the triangle), this vertical line will intersect the graph of the triangle more than once. So, Graph C does not pass the vertical line test and is a non - function (a relation).

Answer:

C. The graph of the triangle (Graph C)