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 grid with no curve, b is a parabola opening to the right, c is a parabola opening downward, d is a circle centered at the origin.)

Accepted Answer

d

Answer

Step 1: Recall the vertical line test rule for functions: A graph represents a function if and only if no vertical line drawn on the graph intersects the graph at more than one point. Step 2: Analyze graph a: Since there is no plotted relation, it trivially satisfies the vertical line test (or represents an empty function, which is a function). Step 3: Analyze graph b: The right-opening parabola will have each vertical line intersect it at most once, so it is a function. Step 4: Analyze graph c: The downward-opening parabola will have each vertical line intersect it at most once, so it is a function. Step 5: Analyze graph d: Draw a vertical line through the circle (e.g., x=2). This line intersects the circle at two points, violating the vertical line test. So this relation is not a function.