The TI-86 Calculator

Graphing Functions

There are four steps to graphing a function. We will illustrate this procedure using examples of the different types of functions that we will encounter in College Algebra this semester.

GRAPH the polynomial function f(x) = x³ + 2x² - 3x - 6

press GRAPH;

choose the y(x)= option (F1) in the GRAPH menu;

enter the function's definition by using the following key sequence:

The calculator will display \y1=x^3+2 x²-3 x-6 (note how similar this is to the expression above)

press the EXIT key and then choose the GRAPH option (F5) in the GRAPH menu;

The graph should then be displayed in the standard display window as shown below (press the CLEAR key if you want to remove the menus):

If you do not have the standard display window then choose GRAPH/ZOOM/ZSTD

GRAPH the absolute value function f(x) = |2x - 5|

press GRAPH;
choose the y(x)= option (F1) in the GRAPH menu;
if you still have y1 defined unselect it using the SELCT (F5) option in the y(x)= menu and press the down arrow to enter the function's definition for y2 using the following key sequence:
A B S
The calculator will display \y2=ABS (2 x-5).
press the EXIT key and then choose the GRAPH option (F5) in the GRAPH menu;

The graph should then be displayed in the standard display window as shown below:

GRAPH the rational function f(x) =

A better way to write this is: f(x) = (4x² - 9)/(2x² + 1). The parenthesis are very important here. They are used to delimit the numerator and denominator of the fraction.

press GRAPH;
choose the y(x)= option (F1) in the GRAPH menu;
if you still have y1 defined unselect it or delete it using either the CLEAR key or the DELF option on the y(x)= menu. Enter the function's definition The calculator should display \y1=(4 x² - 9)/(2 x² + 1). (Note the use of parenthesis to delimit the numerator and denominator. This is very important).
press the EXIT key and then choose the GRAPH option (F5) in the GRAPH menu (or you could use the second function of F5 to graph it);

The graph should then be displayed in the standard display window as shown below:

GRAPH the radical function f(x) =

Another way to write this is: f(x) = (x² - x - 20)^1/2. The parenthesis are very important here. They are used to delimit the radicand of the radical.

press GRAPH;
choose the y(x)= option (F1) in the GRAPH menu;
Enter the function's definition. The calculator should display \y1=(x² - x - 20)^(1/2). (Note the use of parenthesis to delimit the radicand and the exponent. These are very important).
press the EXIT key and then choose the GRAPH option (F5) in the GRAPH menu (or you could use the second function of F5 to graph it);

The graph should then be displayed in the standard display window as shown below:

GRAPH the logarithmic function f(x) = log₁₀ (x)

press GRAPH;
choose the y(x)= option (F1) in the GRAPH menu;
Enter the function's definition. The calculator should display \y1=log (x).
press the EXIT key and then choose the GRAPH option.

The graph should then be displayed in the standard display window. This view of the graph is not too clear since the negative part of the graph is plotted over a very small interval and the positive values are very small in this window. We can get a better view of the graph by choosing GRAPH/ZOOM/ZFIT (use the MORE key to get to ZFIT in the ZOOM menu). The window changes to display the function values in the range -.8 to 1 (note that ZFIT does not changes the domain of x values that are selected.)

GRAPH the logarithmic function f(x) = log₂ (x)

press GRAPH;
choose the y(x)= option (F1) in the GRAPH menu;
Enter the function's definition. Since there is no base 2 log function on the calculator we need to write it in terms of the base 10 log we do have. So enter the definition log(x)/log(2). The calculator should display \y1=log (x)/log (2).
press the EXIT key and then choose the GRAPH option.

The graph should then be displayed in the standard display window. This view of the graph is not too clear since the negative part of the graph is plotted over a very small interval and the positive values are very small in this window. We can get a better view of the graph by choosing GRAPH/ZOOM/ZFIT (use the MORE key to get to ZFIT in the ZOOM menu). The window changes to display the function values in the range -2.7 to 3.3 (note that ZFIT does not changes the domain of x values that are selected.)

GRAPH the exponential function f(x) = e^{x² + 1}

press GRAPH;
choose the y(x)= option (F1) in the GRAPH menu;
Enter the function's definition. Be careful to use parenthesis to delimit the exponent. The calculator should display \y1=e^(x² + 1).
press the EXIT key and then choose the GRAPH option.

The graph should then be displayed in the standard display window. If not then choose GRAPH/ZOOM/ZSTD. This view of the graph is ok but much of the display is wasted. It would be better just to look at the graph for small values of x. Use GRAPH/WIND to set xMin=-2, xMax=2, and since there are no negative values for this function set yMin=-1. We get: