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x y 6 (5, 3) 6 6 6 (3, 2) (4, 0) (5, 3) x y 6 (4, 3) (3, ) 52 (2, 0) (0, 1) 6 6 6 (4, 1) Example 1a) Example 1b) not a function is a function The relation in Example 1a) is not a function since the x-value of 5 corresponds to two different y-values, 3 and 3. Notice that we can draw a vertical line that intersects the graph in more than one point—the line through (5, 3) and (5, 3). The relation in Example 1b), however, is a function—each x-value corresponds to only one y-value. Here we cannot draw a vertical line through more than one point on this graph. This leads us to the vertical line test for a function. Procedure The Vertical Line Test If there is no vertical line that can be drawn through a graph so that it intersects the graph more than once, then the graph represents a function. If a vertical line can be drawn through a graph so that it intersects the graph more than once, then the graph does not represent a function. EXAMPLE 2 Use the vertical line test to determine whether each graph, in blue, represents a function. a) b) x y 5 5 5 5 x y Solution a) Anywhere a vertical line is drawn through the graph, the line will intersect the graph only once. This graph represents a function. b) This graph fails the vertical line test because we can draw a vertical line through the graph that intersects it more than once. This graph does not represent a function. We can identify the domain and range of a relation or function from its graph. x x In-Class Example 2 Use the vertical line test to determine whether each graph represents a function. a) y 5 5 5 y 5 5 b) 5 5 5 Answer: a) function b) not a function 642 CHAPTER 10 Quadratic Equations www.mhhe.com/messersmith


messersmith_power_introductory_algebra_1e_ch4_7_10
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