Section 3.6 Functions 269 These illustrations provide us a method for determining if a relation is a function by examining its graph. This method involves performing the vertical line test. �������������������� Vertical Line Test 1. If all vertical lines drawn on the graph of a relation intersect the graph in at most one point, then the graph is a function. 2. If at least one vertical line intersects the graph in more than one point, then the graph is not a function. �� ������������������������ ������������������ Use the vertical line test to determine if each relation is a function. 3a. 3b. 3c. 6 4 Solutions 3a. The relation graphed is a function since every vertical line intersects the graph in at most one point. 2 2 4 6 –2 –4 x y 3b. The graph is not a function since a vertical line through x = -3 intersects infinitely many points of the graph. 2 2 4 4 –2 –4 –2 –4 x y 3c. The graph is not a function since any vertical line drawn between the x-values of -2 and 2 intersects the graph in two points. 4 2 4 –2 –4 –4 x y 2 2 4 4 6 –2 –2 –4 x y 2 2 4 4 –2 –4 –2 –4 x y 2 4 –2 –4 –4 x y
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