268 Chapter 3 Linear Equations in Two Variables Student Check 2 Determine if each relation is a function. If not, explain why. a. {(5, 1), (5, -2), (5, 6), (5, 3), (5, 0)} b. {(1, 5), (-2, 5), (6, 5), (3, 5), (0, 5)} c. Let the relation be defined by the mapping, where x is the student and y is the grade earned in math class. Student Grade A B C D F Angela Aretha Dylan Edward Ginger Hunter Natalia d. y = x2 Vertical Line Test We will now examine graphs of relations and see how we can use them to determine if a graph represents a function. Graphing some of the preceding examples will show us an important characteristic of the graph of a function. Shown next are some examples of functions and their corresponding graphs. y = uxu 2 2 4 4 –2 –4 –2 –4 x y 2 2 4 4 –2 –4 –2 –4 x y If each x-value corresponds to only one y-value, we know the relation is a function. Notice that when we draw vertical lines through the graph of the relations, each vertical line touches the graph only once. Shown next are examples of relations that are not functions. x = y2 (–3, 2) 2 (–4, 0) (0, –4) (–3, –2) (0, 4) 2 4 –2 –6 –4 –2 –4 x y 4 2 –2 –6 –2 –4 x y Notice that when an x-coordinate is paired with more than one y-coordinate, a vertical line can be drawn that will intersect the graph at more than one point. Objective 3 ▶ Use the vertical line test. {(-2, -3), (-1, -3), (0, -3), (1, -3), (2, -3), (3, -3)} {(-4, 0), (-3, 2), (-3, -2), (0, 4), (0, -4)}
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