Question 8.3.9: Graph the inequality 27y³ ≤ 8+x³....
Graph the inequality 27y³ ≤ 8+x³.
Inequality: 27y³ ≤ 8+x³.
Final Answer
We must first solve the associated equality for y:
We assign \frac{1}{3} \sqrt[3]{8+x^3} \text {to} Y_1 \text {and graph} Y_1 in the viewing rectangle [-6, 6] by [-4, 4] , as shown in Figure 12. The test point (0, 0) is in the solution region (since 0 ≤ 8 is true), so we want to shade the region below the graph of Y_1. The commands for the TI-83/4 Plus are shown.
The parameters for the Shade command are as follows:
-4 is the lower function for the shaded region – in this case, we simply use the value of Ymin. Y_1 is the upper function for the shaded region.
-6 and 6 are Xmin and Xmax.
1 is the shading pattern; there are four of them.
3 shades every third pixel; you may specify an integer from 1 to 8 .
Pressing \boxed {\text {ENTER}} gives the following graph.
Alternative Method: There is an alternative method for shading available. It can be executed by selecting a graphing style from the \boxed {Y=} screen.
Using the cursor keys, move the cursor to the left of ” Y_1.” Successively press \boxed {\text {ENTER}} to cycle through the seven graphing styles. Select the “shade below” style as shown in the figure. Pressing \boxed {\text {GRAPH}} produces a shaded figure as before.
