MATH 1351 TI-85 EXERCISE III

Building a custom catalog

Name: SIN:

There are a lot of functions, programs, operations, etc. in the TI-85 that are not directly accessed from the keyboard. Some of these will be useful to us throughout this course. They can be accessed by pressing 2nd CATALOG from the keyboard, then arrow down until the particular thing you are seeking is indicated by the little wedge at the left of the screen. However, there are a lot of things in the main catalog. In fact, choose PAGE down from the screen menu until you have seen the entire catalog. As you can see there must be a gazillion things in this catalog and you don't want to have to page through it every time you want to use something near the end; tanh, for example. Fortunately we can place those things we use a lot into a custom catalog. For example, find abs in the catalog and use the up/down arrow keys to designate it with the little wedge. Choose CUSTM from the screen menu and press the F key under an empty space in the custom screen menu. Next find int in the catalog and put it into an empty space in your custom menu. Henceforth to access abs or int you need only choose CUSTOM from the keyboard and the appropriate F key.

Now let's figure out just what these two functions do. Sketch the graph of the function

y = abs (x).

Use TRACE to compare the values of x and abs (x). Explain what this function appears to be doing to numbers.

Next sketch the graph of the function y = int (x). This picture may be misleading, let's try a different graphing format. Choose FORMT from the GRAPH menu. Arrow down until the DrawLine command is flashing then over to DrawDot. Pressing ENTER changes to the DrawDot format. Meaning, only the points on the graph are lighted and no attempt is made to connect them with lines. Now choose GRAPH from the GRAPH menu and sketch the new picture.

Use TRACE in the ZDECM viewing window to compare the values of x and int (x). Explain what this function appears to be doing to numbers.

How would you describe the behavior of the function "at each integer?"

Graph each function in # 1, 2, & 3. Zoom in on the origin and explain in your own words what is happening "near the origin" on each graph.

1. y = x^2 + abs(x)

2. y = x ^3 + abs(x)

3. y = sin x

In # 4 - 9 we investigate the results of some compositions on the graphs. Attach a sketch of the graphs of each of the following functions. Use DrawDot format to get a good picture. Remember that the actual graphs of functions can not have vertical lines in them. Why not?

4. y = sin (abs (x) )	5. y = abs (sin (x) )	6. y = sin ( int (x) )

7. y = abs (x^3)	8. y = (int(x))^2	9. y = int(x^2)

In # 10, 11, & 12 we investigate the results of adding functions. Attach a sketch of the graphs of each of the following functions.

10. y = x + int(x)	12. y = x - int(x)	13. y = abs(x) - int(x)

In # 14 try choosing ZDECM viewing window, and DrawDot format. Investigate the graph in #14 for x values at all multiples of ½. Provide a description and explanation of what you observe.

14. y = int ( sin (Pi x) ) +2