Helpful Tools for Calculus, Chapter 0: Numbers, Notations and Notes
Previous Section: 0.8 Patterns
As of the writing of this text, the most commonly used and one of the best overall graphing calculators is the Texas Instruments TI-84 model calculator. This section will introduce the reader to some helpful tools on the TI-84 calculator and things that will be used frequently in this text.
Solving Expressions
The first thing to feel comfortable with on any calculator is how to solve an expression with it. Generally, calculators are pretty good at using the order of operations. Being clear with grouping is the most important thing to pay attention to in order to avoid mistakes.
Take the following examples:
The same numbers with four different patterns of parenthesis result in four different solutions. Using parenthesis to group the top and bottom of a fraction is really important to avoid changing problems into something else. So, adding parenthesis to your written work for clarity, before plugging into a calculator, will be helpful.
In addition to using parenthesis intentionally for grouping, try to ensure that parenthesis are used to close functions like trigonometric functions, logarithms and other things that have an input:
One more common mistake is using the negative and subtraction symbols interchangeably. In written work, they look the same so it is okay to present ‘three minus negative two’ as 3–2 when a more appropriate form would actually be 3-–2. However, on a calculator this can cause a few different problems:
Typing minus three (-3) will try to subtract it from the previous answer (in this case it was 0) while typing negative three (-3) will just evaluate it as negative 3. Typing –– 3 will subtract negative 3 from the previous answer. Finally, just typing minus 3 will result in a syntax error.
Graphing Functions
In order to graph equations on a graphing calculator, we need to press the “y=” button found at the top left. You will be greeted with a screen like the following:
Each of these YN represent a different equation. If the equal sign is highlighted, like in Y1 and Y3, then that equation is active and will be graphed. Y2 is inactive, so it won’t be graphed, while Y4 is inactive because no equation has been typed there. Additionally, to the left of the YN is a color and a line. The line indicates how it will be presented on the graph. The standard is a solid line, while in this example Y3 is graphed with the bottom half shaded.
These can be changed by clicking the ‘enter’ button while it is highlighted. Clicking the ‘graph’ button and the ‘trace’ button will both open the graphing window, as shown above. The difference is that ‘trace’ allows you to interact with the graph. Tracing the graph allows a dot to appear on the curve which can be moved by pressing the left and right buttons on the directional pad. Pressing the up and down buttons will switch between the active graphs, which is indicated in the top left of the window.
While in trace mode, it is also very easy to input numbers into the function! You can simply type a number, which will appear on the bottom of the screen, then click enter to plug it into the function. When possible the calculator will put a dot on the point and tell you the output! This is very helpful when you need to plug many different numbers into one equation.
Adjusting the Window
You may notice while graphing that not all functions fit the viewing screen perfectly. There are a few options to fix that. One option is to click the ‘zoom’ button at the top center and choose from one of the options. There are a number of built in presets which may be helpful. Otherwise, you may need to manually set the window to see something specific. Clicking the ‘window’ button will bring up this screen:
Xmin describes the smallest x-value visible on the screen. This is also the left edge of the window. Xmax is the right edge of the window. Xscl describes how it is counting, so if it equals 1 then the little marks on the axis will count by ones. Ymin, Ymax and Yscl are exactly the same, but in the vertical direction. ∆X describes how the calculator will choose points to evaluate on the curve. I don’t recommend adjusting this value. The calculator will often automatically adjust it as needed. The same thing is true of TraceStep.
This is a possible window for the graph of 
Other Operations
There are a quite a few more thing that the calculator is capable of. However, for most students of calculus, the only other tools that may be helpful can be found by pressing the button labelled ‘math’.
There are a few tabs, visible at the top, and the selected one will appear highlighted. In this case ‘MATH’ is the selected tab. These include a variety of helpful tools. Options 1 and 2 convert to a fraction or a decimal form (if possible). Option 5 allows the user to enter a root function with any number root desired, like √(13&5). This is also where you can find buttons for summation, logarithms with any base, lowest common multiple, greatest common divisor, remainder, converting between fraction forms, factorials, and more.
I would encourage students to play around with and explore the buttons on the calculator to be acquainted with anything else they may find helpful or interesting. We have really only scratched the surface of what these machines are capable of.