Section 1: Exponents and Roots

760 Chapter 8 Exponential and Logarithmic Functions◮ Example 21. Find all real solutions of the equation x 2 = 7, both graphically andalgebraically, and compare your results.We could easily sketch rough graphs of y = x 2 and y = 7 by hand, but let’s seek ahigher level of accuracy by asking the graphing calculator to handle this task.• Load the equation y = x 2 and y = 7 into Y1 and Y2 in the calculator’s Y= menu,respectively. This is shown in Figure 5(a).• Use the intersect utility on the graphing calculator to find the coordinates of thepoints of intersection. The x-coordinates of these points, shown in Figure 5(b) and(c), are the solutions to the equation x 2 = 7.(a) (b) (c)Figure 5. The solutions of x 2 = 7 are x ≈ −2.645751 or x ≈ 2.6457513.Guidelines for Reporting Graphing Calculator Solutions. Recall the standardmethod for reporting graphing calculator results on your homework:• Copy the image from your viewing window onto your homework paper. Label andscale each axis with xmin, xmax, ymin, and ymax, then label each graph with itsequation, as shown in Figure 6.• Drop dashed vertical lines from each point of intersection to the x-axis. Shade andlabel your solutions on the x-axis.10yy=x 2 y=7−10 −2.645751 2.6457513 10x−10Figure 6. The solutions of x 2 = 7 arex ≈ −2.645751 or x ≈ 2.6457513.Version: Fall 2007