# Calculators in UTM Mathematics Courses

 Several of the mathematics courses at the University of Tennessee at Martin require a graphing calculator: 140 185 251 and 252.  If you do not have a graphing calculator, then for 140 we recommend the TI83. For other courses check with your teacher.  If you do have a graphing calculator, it will probably be just fine--check with your teacher.  If possible, do not buy your calculator in the college bookstore. Calculators cost substantially less at the local Walmart.

## Graphing Using the TI Graphing Calculators

### Greatest Integer Function

To graph greatest integer functions on the TI 82, TI 85, and TI 86 you need to be in Dot Mode.
On the TI 83 you need to graph in Connected Mode first, then switch to Dot Mode.

On the TI 82 and TI 83 press the MODE button. Use the down arrow to move the cursor to
CONNECTED. Now use the right arrow to move the cursor to DOT and press ENTER.
You will now be in Dot Mode.

On the TI 85 and TI 86 first press GRAPH then MORE. At this point you should see FORMT on
the menu bar at the bottom of the screen. Press F3, then use the down arrow to move the cursor to
DRAWLINE. Next use the right arrow to move the cursor to DRAWDOT and press ENTER.
You will now be in Dot Mode.

To graph greatest integer functions on the graphing calculator you will need to use INT

To locate INT on the TI 82 and the TI 83 start by pressing MATH then use the right arrow to
move the cursor to NUM then use the down arrow to move the cursor to INT.

To locate INT on the TI 85 and the TI 86 start by pressing 2nd then MATH. You now have a menu bar at the bottom

Press F1 and now you have a second menu bar showing and INT is the fourth item so you press F4.

Example: graph

Using the TI 82 or TI 83 start by pushing Y= this will get you to the screen where equations are put in for graphing. On the TI 85 you push the button that says GRAPH. Now you need to locate and enter INT followed by (x+1). your problem should look like

### Piecewise Defined Functions

To graph multi-part functions on the graphing calculator you will need to use the TEST button. To access the TEST button on all three calculators you will need to use the 2nd button. This will give you a list of inequality symbols that will be needed to graph multi-part functions.

We will use <= to symbolize less than or equal to, and => to symbolize greater than or equal to in the following material.

In graphing piecewise defined functions it is best to be in Dot Mode.

On the TI 82 and TI 83 press the MODE button. Use the down arrow to move the cursor to CONNECTED. Now use the right arrow to move the cursor to DOT and press ENTER. You will now be in Dot Mode.

On the TI 85 first press GRAPH then MORE. At this point you should see FORMT on the menu bar at the bottom of the screen. Press F3, then use the down arrow move the cursor to DRAWLINE. Next use the right arrow to move the cursor to DRAWDOT and press ENTER. You will now be in Dot Mode.

Example graph:

2x+1, x<=-3
f(x)= 3x+2, -3<x<1
x^2-2, x=>1

Using the TI 82 or TI 83 start by pushing Y=. Now enter the following(2x+1)(x at this point press 2nd then TEST then 6, this will give you the less than or equal symbol. Now finish with -3). The equation should look like

Y1=(2x+1)(x<=-3)

Using the TI 85 start by pushing GRAPH. Now enter the following(2x+1)(x at this point press 2nd then TEST then F4, this will give you the less than or equal symbol. Now finish with -3)The equation should look like

Y1=(2x+1)(x<=-3)

To do the middle part, 3x+2, -3<x<1, on the TI82, TI83, TI85, enter the following (3x+2)(-3 at this point access the TEST button and enter the appropriate symbol. Now finish with x)(x again access TEST button and use the appropriate symbol. Now finish with 1) The equation should look like

Y2=(3x+2)(-3<x)(x<1)

The third part of this multi-part function is done the same way the first part was done. The equation should look like

Y3=(x^2-2)(x=>1)

### Absolute Value Functions

To graph absolute value on the graphing calculator you will need to use the ABS button.

On the TI 82 you access the ABS button by first pressing 2nd.

On the TI 83 you access ABS by pressing MATH, then using the right arrow move the cursor to NUM

On the TI 85 you access ABS by pressing 2nd then MATH, this gives you a menu bar at the bottom. Now press F1 under NUM. This will give you another menu bar and ABS is located at F5.

Example: graph y = -1(1 + absolute value of x)

Start by pressing Y=(for the TI 82 and TI 83) or GRAPH(for the TI 85) then enter the following-1(1+ at this point you need to access ABS according to the calculator you are using. If you are using a TI 82 or TI 85 finish with x). If you are using a TI 83 finish with x))Your equation should look like

Y1=-1(1+abs x) for the TI 82 and TI 85
Y1=-1(1+abs (x)) for the TI 83