SECTION 1.1 Graphing Utilities; Introduction to Graphing Equations 9 4 Find Intercepts from a Graph The points, if any, at which a graph crosses or touches the coordinate axes are called the intercepts . See Figure 19. The x -coordinate of a point at which the graph crosses or touches the x -axis is an x-intercept , and the y -coordinate of a point at which the graph crosses or touches the y -axis is a y-intercept . For a graph to be complete, all its intercepts must be displayed. In looking at Table 3 on the previous page, notice that = y 12 when = x 0. This information could have been used to help create the initial viewing window by letting us know that Ymax needs to be at least 12 in order to get a complete graph. Both Desmos and Geogebra allow a user to create a table of values as well. Figure 18 shows a table of values and graph using Geogebra where eq1(x) is + = x y 6 3 36. 2 Figure 18 eq1(x): x y 6 3 36 2 + = Figure 20 x y (0, 3) (23, 0) , 0 (0, 2 ) 3 – 2 (4.5, 0) (0, 23.5) 4 24 5 4 – 3 ( ) Figure 19 Intercepts x y Intercepts Graph touches x-axis Graph crosses x-axis Graph crosses y-axis Solution The intercepts of the graph are the points ( ) ( ) ( ) ( ) ( ) ( ) − − − 3, 0 , 0, 3 , 3 2 , 0 , 0, 4 3 , 0, 3.5, 4.5, 0 The x -intercepts are −3, 3 2 , and 4.5; the y -intercepts are − − 3.5, 4 3 , and 3. In Example 7 notice the following usage: If the type of intercept is not specified ( x - versus y -), then report the intercept as an ordered pair. However, if the type of intercept is specified, then report the coordinate of the specified intercept. For x -intercepts, report the x -coordinate of the intercept; for y -intercepts, report the y -coordinate of the intercept. Now Work PROBLEM 37 5 Use a Graphing Utility to Approximate Intercepts We can use a graphing utility to approximate the intercepts of the graph of an equation. Finding Intercepts from a Graph Find the intercepts of the graph in Figure 20. What are its x -intercepts? What are its y -intercepts? EXAMPLE 7 Approximating Intercepts Using a Graphing Utility Use a graphing utility to approximate the intercepts of the equation = − y x 16. 3 Solution EXAMPLE 8 On the next page, Figure 21(a) shows the graph of = − y x 16. 3 The eVALUEate feature of a TI-84 Plus CE graphing calculator accepts as input a value for x and determines the value of y. If we let = x 0, the y -intercept is found to be −16. See Figure 21(b) on the next page. In Words Intercepts are points (ordered pairs). An x -intercept or a y -intercept is a number. For example, the point 3, 0 ( ) is an intercept; the number 3 is an x -intercept. (continued)
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