Question

which of the following does not represent a function?
o a
o b
o c

Explanation:

Step1: Recall function - vertical line test

A relation is a function if for every \(x\) - value there is exactly one \(y\) - value. The vertical - line test is used to determine if a graph represents a function. If a vertical line can be drawn that intersects the graph at more than one point, then the graph does not represent a function.

Step2: Analyze graph a

For graph a (a V - shaped graph, an absolute - value function), any vertical line drawn will intersect the graph at most once. So, it represents a function.

Step3: Analyze graph b

For graph b (a parabola opening to the left), a vertical line can be drawn that will intersect the graph at two points. For example, a vertical line near the vertex of the parabola will cross the graph in two places. So, it does not represent a function.

Step4: Analyze graph c

For graph c (an ellipse), a vertical line can be drawn that will intersect the graph at two points. For example, a vertical line passing through the center of the ellipse will cross the graph in two places. So, it does not represent a function.

Answer:

B. Graph b, C. Graph c