Identify Which Graph Does Not Represent a Function (Vertical Line Test Practice)

Question

Which of the following relations is not a function? (There are four graphs labeled a, b, c, d: a is a set of points with no overlapping x-values, b is a parabola opening to the right, c is a parabola opening upwards, d is a circle centered at the origin)

Accepted Answer

Graph d

Answer

Step 1: Recall the vertical line test, the rule to determine if a graph represents a function: if any vertical line drawn on the graph intersects the graph at more than one point, the relation is not a function. Step 2: Apply the vertical line test to each graph: 
- Graph a: Any vertical line intersects at most one point, so it is a function.
- Graph b: Any vertical line intersects at most one point, so it is a function.
- Graph c: Any vertical line intersects at most one point, so it is a function.
- Graph d: A vertical line (e.g., x=2) will intersect the circle at two distinct points, which violates the vertical line test. Step 3: Conclude that graph d is the relation that is not a function.