## Section 19 for the TI-84C

Some of these operations you should be familiar with on the TI-83 are listed below.

As a student continues their study of mathematics in an Advanced Placement Calculus class the graphing calculator will continue to help the student build a deeper understanding for the function numerically and graphically.  Once the student has developed these two foundational viewpoints the student will have less difficulty understanding the analytically study of the same mathematical concepts.

It doesn't matter which graphing calculator you use, all of the following skills are important on any graphing calculator.

1. Working with the calculator in the correct mode

Function Mode: (Func)

In most cases the student will want to make sure their calculator is in the Function mode.  Although there will be a few times when parametric, polar, and sequence mode will also be used.

Sequential Mode vs. Simultaneous Mode:

It usually does not matter which of these two modes a student selects.  Each has their advantages--you should study how two functions are graphed under each of these modes and make your choice as which one you would use in a particular situation.

Floating Decimal Point:

Students should round off all their final answers to THREE decimal places, but this means that throughout a problem a student should work with more than three decimal places (possibly five).  Then when the final answer is stated the answer should be rounded to THREE decimal places.

Dot vs. Connected Mode:  Students should realize that they are working with a discrete calculator which locates a finite number of points associated with a function and connects these finite number of points to create a smooth graph (connected mode). As a student traces along the graph they can read the values of x the calculator used to generate the representative graph.  If a student places a calculator in dot mode they will see the set of points the calculator generated to create a picture of the graph.

2.  Window dimensions:

The graphing calculator can graph a function in many different windows.  You can select minimum and maximum x- and y-values.  Most graphing calculators allow you to view a graph in a standard window {-10, 10, 1, -10, 10, 1}, but this is not necessary the best window to view all functions.  For example the function y=sin x would be better viewed in a window {-8.63, 8.63, 1, -4, 4, 1}.  Students should consider the behavior of a function and its range in building a window.

The TI-83 graphing calculator does have one zoom feature which makes building a window easy.  It is 0:  ZoomFit.  You must first select a domain and then the calculator will determine what function values are needed to view the entire graph.  Suppose you had the equation and wanted to view it in the domain .  First enter the equation in a y-slot and then set Xmin=0, Xmax=10, and Xscl=1.  Press Zoom, and select choice 0:  ZoomFit.

From the graph you can see that the function takes on many negative function values:  .  But it is not real clear what the function is doing about x=0.  To view the behavior around x=0 change Xmax=2 and re-build a window using ZoomFit.

This view shows the behavior the function between .

3.     Table set and Table

To study a function numerically a student will often build a table.  To build a table automatically the student must tell the calculator the minimum value of x in the table and the increments between the x values.

Once these values are selected, and the student selects TABLE, the calculator can build an automatic table.

If a student wants to build a table with x values which are not equally spaced they may elect to build a table by ask mode.  When this mode is selected, and the student selects TABLE the student will input the x values and the calculator will determine the corresponding y-values for the selected x-values.

4.  Y= Key

When a student enters an equation in one of the function slots, the calculator will graph the equation in the selected window.   Very often a student forgets that an equation has been entered in one of the slots when working on a graph in a statistical mode.  These equations can be turned off so they don't graph at an inappropriate time.

5.    Stat Plots

From the Y= screen it is possible to tell if a statistical plot is turned on or off.  Always check the top of the screen to see if any of the STAT Plots are turned on before graphing an equation.

6.     Returning to the Home Screen

Students should know that 2nd Quit will always return them to the HOME screen for entering numerical calculations and commands.

7.    Entering numerical expressions

In most cases the graphing calculator usually follows the order of operations learned by most students as part of a pre-algebra course.  But there are a few exceptions.  Students should practice entering some of the following expressions to see whether they get the correct values. (Answer have been rounded off to three decimal places of accuracy.)

 Expression Answer -2 ~1.754 -32 ~.374 ~-0.180

Check Your Understanding:   Build an appropriate window to view each of the following graphs.  Be prepared to explain why you have selected each window.  In some questions a dot mode should be selected, while in other cases the connected mode should be selected.  The graph should show the behavior of the function for the given domain.

1. Graph the function for the real numbers -20 < x < 20.  After graphing the function in the given domain, find the value of y(100).

2. Graph the rational function for the real numbers -0.5 < x < 4.  After graphing the function in the given domain, find the value of y(4)-y(2).

3. Graph the function for the real numbers 1 < x < 10.  After graphing the function in the given domain, find the value of

4. First graph the function for the real numbers 1 < x < 5.  Then set up a table to find the values of  for the values x = 2.4, 2.5, 2.6, 2.7, 2.8, 2.9 and 3.

Rev. 03/21/16