SECTION 1.1 Graphing Utilities; Introduction to Graphing Equations 7 Figure 13 Y x2 12 1 2 =− + 10 210 210 10 Figure 11 How to Graph an Equation Using a Graphing Utility Use a graphing utility to graph the equation: x y 6 3 36 2 + = EXAMPLE 5 Step-by-Step Solution Step 1 Solve the equation for y in terms of x. x y y x y x 6 3 36 3 6 36 2 12 2 2 2 + = = − + = − + Step 2 Enter the equation to be graphed into your graphing utility. Figure 11 shows the equation to be graphed entered on a TI-84 Plus CE. Step 3 Choose an initial viewing window. Without any knowledge about the behavior of the graph, it is common to choose the standard viewing window as the initial viewing window. The standard viewing window is X Y X Y Xscl Yscl min 10 min 10 max 10 max 10 1 1 =− =− = = = = See Figure 12. Step 4 Graph the equation. See Figure 13. Step 5 Adjust the viewing window until a complete graph is obtained. The graph of y x2 12 2 = − + is not complete. The value of Ymax must be increased so that the top portion of the graph is visible. After increasing the value of Ymax to 12, we obtain the graph in Figure 14. The graph is now complete. Now Work PROBLEM 45 NOTE Some graphing utilities have a ZOOM-STANDARD feature that automatically sets the viewing window to the standard viewing window. In addition, some graphing utilities have a ZOOM-FIT feature that determines the appropriate Ymin and Ymax for a given Xmin and Xmax. Consult your user’s manual for the appropriate keystrokes. j Subtract x6 2 from both sides. Divide both sides by 3 and simplify. Figure 12 Standard viewing window We are now ready to graph equations using a graphing utility. Figure 14 Y x2 12 1 2 =− + 12 210 210 10
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