8 CHAPTER 1 Graphs 3 Use a Graphing Utility to Create Tables In addition to graphing equations, graphing utilities can also be used to create a table of values that satisfy the equation. This feature is especially useful in determining an appropriate viewing window when graphing an equation. Look again at Figure 14 on the previous page. Although a complete graph is shown, the graph might be improved by adjusting the values of Xmin and Xmax. Figure 15 shows the graph of y x2 12 2 = − + using Xmin 4 = − and Xmax 4. = Some graphing utilities do not require the equation be written in the form “y x expression in . { } = ” Figure 16 shows the graph of x y 6 3 36 2 + = using Desmos. Figure 15 Y x2 12 1 2 =− + 12 210 24 4 Figure 16 x y 6 3 36 2 + = Figure 17 Table setup Step-by-Step Solution Step 1 Solve the equation for y in terms of x. Create a table using AUTO mode. The table we wish to create starts at −3, so TblStart = −3. The increment for x is 1, so Δ = Tbl 1. See Figure 17. Step 2 Enter the expression in x following the “Y =” prompt of the graphing utility. See Figure 11 on the previous page. Step 3 Set up the table. Graphing utilities typically have two modes for creating tables. In the AUTO mode, the user determines a starting point for the table (TblStart) and Tbl Δ (pronounced “delta table”). The Tbl Δ feature determines the increment for x in the table. The ASK mode requires the user to enter values of x, and then the utility determines the corresponding value of y. Step 4 Create the table. See Table 3. How to Create a Table Using a Graphing Utility Create a table that displays the points on the graph of x y 6 3 36 2 + = for x 3, 2, 1, 0, 1, 2, = − − − and 3. We solved the equation for y in terms of x in Example 5 and obtained = − + y x2 12. 2 EXAMPLE 6 In AUTO mode, the user can scroll forward or backward within the table to find additional values. Table 3
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