Page 182

hendricks_intermediate_algebra_1e_ch1_3

180 Chapter 3 Graphs, Relations, and Functions Note: Example 1 illustrates two important facts. 1. When the x-values of a relation repeat, the relation is not a function. 2. The y-values of a function can repeat. The Vertical Line Test Now we will examine graphs of relations and learn how we can determine if they represent a function. Some examples of functions and their corresponding graphs are shown. 5(-2, -3), (-1, -3), (0, -3), y = |x| (1, -3), (2, -3), (3, -3)6 2 2 4 4 –2 –4 –2 –4 x y 2 2 4 4 –2 –4 –2 –4 x y Notice that in the graph of these functions, each x-value corresponds to only one y-value, as shown by the vertical lines. Some relations that are not functions and their corresponding graphs are shown. 5(-4, 0), (-3, 2), (-3, -2), x = y2 (0, 4), (0, -4)6 (–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 in these graphs that are not functions, there are values of x that have more than one corresponding y-value, as shown by the vertical lines. We can use the facts shown in these illustrations to determine if a relation is a function by examining its graph. We can determine if a graph represents a function by performing the vertical line test. Procedure: Using the Vertical Line Test Step 1: Draw vertical lines through the graph of the relation. Step 2: Determine how many times each vertical line intersects the graph of the relation. a. If each vertical line intersects the graph in at most one point, then the graph is a function. b. If at least one vertical line intersects the graph in more than one point, then the graph is not a function. Objective 2 ▶ Use the vertical line test.


hendricks_intermediate_algebra_1e_ch1_3
To see the actual publication please follow the link above