GRAPH

To construct graphs and use graphical analysis commands, use the Graph menu. From the Main Menu, press 5.

The first screen is the function/relation editor. To select how certain results will be displayed, press SHIFT MENU (SET UP). The suggested selections for Coord, Grid, Axes and Label are shown. Scroll down to these selections.

To make a change, highlight the item and use the function button that appears directly below the desired tab. For example, when Coord is highlighted, F1 (On) will turn coordinates on and F2 (Off) will turn coordinates off. Press EXIT to return to the editor.

The Math Club plans to sell t-shirts. Previous experience suggests that the number of t-shirts sold depends on the price. A good model for the number sold, y, as a function of the price, x, is y = -2x + 40.

1. Construct a graph of this equation.

To construct a graph of this model, press Y= (-2x + 40) EXE. To select the view window, press SHIFT F3 (V-Window). Change the values for the window, as shown, pressing EXE after each value. The values for Scale determines the location for the marks on the axes and the gridlines. Press EXIT to return to the editor.

To draw the graph, press F6 (DRAW). When a graph is displayed the + key can be used to zoom in, the - key to zoom out, and the arrow keys to scroll.

2. How many shirts would be sold at a price of $12 per t-shirt?

To trace on the graph, press SHIFT F1 (Trace). Use the arrow keys to move the cursor. To select a specific value, type the value, in this case 12. A dialogue box opens, press EXE. To mark a point and keep the coordinates on the display, press EXE a second time.

The result shows that at a price of $12, 16 shirts are sold.

3. There is a price that is too high, meaning no shirts are sold. This point occurs at the x-intercept of the graph (where y = 0) and the value of x is a root of the equation -2x + 40 = 0.

To find the root, press SHIFT F5 (G-Solv) F1 (ROOT). The result, $20, is shown at the bottom of the screen. To mark this intercept and keep the coordinates on the display, press EXE a second time.

4. If -2x + 40 shirts are sold at price, x, then the number of dollars collected for the sale is x(-2x+40) or -2x² + 40x.

To graph this function, first, deselect the previous equation by pressing EXIT so the cursor is on Y1. Then press F1 (SELECT). Note, the = sign is not highlighted. The cursor should now be on Y2. Press (-) 2 X,Θ,Τ X² + 40 X,Θ,Τ EXE.

5. Compute the number of dollars earned, if each t-shirt is sold at $12.

To compute the number of dollars earned if shirts are sold for $12, press SHIFT F1 (Trace). Type the value, in this case 12. A dialogue box opens, press EXE. The models predict that at a price of $12, 16 shirts will be sold for a total of $192.

6. Determine the price that will give the greatest profit.

To determine the price that is predicted to make the most money, press SHIFT F5 (G-Solv) F2 (MAX). The results, $10 and $200, are shown at the bottom of the screen. To mark the point and keep the coordinates on the display, press EXE.

7. Determine the price of each t-shirt in order to collect $150.

To determine the price of each t-shirt, in order to collect a total of $150, press SHIFT F5 (G-Solv) F6 (X-CAL) 150 EXE. (The ► symbol moves to the next page of commands.)

There is another point where y = 150. Use the arrow keys to move to the next point. Press EXE to mark one or both of these points. $150 can be earned by selling shirts at $5 or at $15.

8. Find the intersection of the equations in Y1 and Y2.

Although it is not particularly meaningful in this example, a common problem is to find the intersection point of two graphs. Press EXIT to return to the editor. Highlight Y1 and press F1 (SELECT). Now, both graphs will be drawn. Press F6 (DRAW). To find the intersection points for the two graphs, press F5 (G-Solv) F5 (INTSECT). 38 shirts are sold at the price of $1, for a total of $38. (These graphs also intersect at (20, 0) where no shirts were sold.)