Before tackling this post, make sure you know how to input functions into your graphing calculator. If you need help with that or just need a reminder, review my blog post called Calculator Help: Input Functions. The very first section in my College Algebra textbook is called "Using Graphing Utilities." The applications portion of the exercise set requires students to find local extrema and intersections of functions. These two tasks are accomplished via the "Calculate" menu on most graphing calculators (TI-83 through TI-89 most specifically). This menu contains many other useful commands and I want to discuss all of them. Today, we'll begin by looking at the first four commands (value, zero, minimum, and maximum). Next time, we will cover commands 5 through 7 (intersect, derivative, and integral).
To find the Calculate menu, press 2ND then TRACE, which is located just below the graphing screen.
Calculator Help: Statistics for instructions on turning on/off stat plots.)
HOW TO USE THE "VALUE" COMMAND
This command requires the input of an x-value and it will determine the y-value at that point. Let's try it out! In the Calculate menu, choose the first command 1: value. The calculator then prompts you for the x-value you want to evaluate. For this command to work, the x-value you enter must be within the viewing window.
Let's evaluate the function at x = 1 (which is in the viewing window of (-4, 8), so it is a valid input). Type in "1" and press ENTER.
The "value" command is very helpful when you need to evaluate a function at a few points. For more than a few points, it is more helpful to consult the table, which we will look at in another post someday.
HOW TO USE THE "ZERO" COMMAND
This command confuses many students. The "zeroes" of a function are the x-values at which the function crosses the x-axis. This occurs whenever the y-value of the function is zero, hence the name. You may also see these values referred to as "x-intercepts." This command will NOT tell you the y-value at which x = 0 (which is the y-intercept). To find the y-intercept, use the "value" command we covered above and input "x = 0." To find the x-intercepts (a.k.a. zeroes) of a function, use the "zero" command. With the same function input into the calculator, return to the Calculate menu and choose the second command 2: zero.
Try finding another zero; say the one in the middle. This time, if you begin at the zero and move left, you will be moving above the x-axis and if you move to the right, you will move below the x-axis. It is very important that, when entering left bound and right bound points, you pay attention to where the graph is located. Left bound will not always be below—as in this case, it is above! You should find this zero to be at the point (0.65, 0).
HOW TO USE THE "MINIMUM" COMMAND
The "minimum" command is used to find a local minimum point, which is the point that forms a "valley" in the graph. With the same function and window set in the calculator, navigate to the Calculate menu and choose command 3: minimum. Visually locate the minimum. This is the point we want to numerically identify.
HOW TO USE THE "MAXIMUM" COMMAND
The "maximum" command is used to find a local maximum point, which is the point that forms a "hill" in the graph. It works exactly as the "minimum" command works. You will move the cursor to the left of the maximum, press ENTER, move the cursor to the right of the maximum, press ENTER again, and then press ENTER once more to move past the guess screen. Here is my answer of (-0.69, 8.60):