Miriam has taught middle- and high-school math for over 10 years and has a master's degree in Curriculum and Instruction.
Evaluating a function and graphing a function are done on different screens of a graphing calculator. This lesson will explain how to do each of these on most Texas Instrument calculators. If you have a different brand of calculator, your screens and buttons may be different.
Evaluating a function can be done on the main calculator screen, the one where you do your usual number operations. Let's go through an example, and I'll explain the steps. We are going to evaluate the function f(x) = 2x^3 - 5x^2 + 4x - 7 when x = 2.
Storing the Value of the Variable
First, we need to store the value of the variable that we want to substitute into the function, the x = 2. We do that by entering 2 and then hitting the button labeled STOR> and then entering a letter (you may need also hit ALPHA before selecting a letter). On some calculators, the x is conveniently located on the same button as STOR>. After you have input the number and the letter under which to store it, you just hit enter. The calculator will show the number, in this example 2, to confirm what you entered.
Entering the Function
Next, you just need to enter the function, leaving off the f(x) = part. Punch in 2x^3 - 5x^2 + 4x - 7 exactly as it is written. Make sure to include the exponents correctly. Since you stored 2 as the x-value, the calculator will automatically insert 2 for every x and evaluate the function. When you hit ENTER after typing in the function, the calculator will display the correct function value of -3.
Just one more important note for evaluating functions on the calculator: Make sure you enter the value of the variable first every time you want to evaluate a new function or a new variable value. If you don't tell the calculator the new value, it will just use the last variable value that was stored. If you don't ever store a value under a particular letter, the default value is 0.
In order to graph functions, you need to use the buttons in the row right underneath the screen. You are going to start with the first button on the left of that row, the one labeled Y=. When you hit that button, you get a screen shown in Figure 1.
Entering the Function
The cursor will be blinking in the row labeled Y1 =. You need to type in the function you want to graph. That function needs to be solved for y and contain only the variable x on the right side of the equation. If your function contains a different variable, you still need to enter x in place of that variable because the calculator does not recognize a different letter while graphing.
So, let's graph the same function we used in the previous example, f(x) = 2x^3 - 5x^2 + 4x - 7. We leave off the f(x) = part and enter 2x^3 - 5x^2 + 4x - 7 right after the Y1 =. Then you have to hit the GRAPH button on the right end of the button row under the screen.
Your calculator will draw the graph. Sometimes, it takes a second or two for the graph to display, depending on how much thinking the calculator needs to do. While it is thinking, you will see a little vertical column on dots in the upper right-hand corner of the screen. Figure 2 shows the graph of the function in this example.
Where's the Graph?
If you are ever trying to graph a function and you don't see anything even after a few seconds, you can try to play with the zoom. If you hit the ZOOM button in the middle of the row right under the screen, you get several options, and you can just hit the number button corresponding to the option you want. The one that says 6: ZStandard will give you a graph with an x-axis from -10 to 10 and a y-axis from -10 to 10. That is usually a good place to start looking for your graph. You can just hit 6 to select that zoom. If that doesn't help, you can try option 0: ZoomFit (you have to scroll down with the arrow keys to see that option). With ZoomFit, the calculator will try to fit the important features of the graph onto the screen.
You can evaluate any function on the main screen of the calculator. First, you have to enter and store the value of the variable. Then, you enter the function, and the calculator will evaluate it for that value.
You graph a function by entering it on the Y= screen. Then, you hit the GRAPH button to display the function. You may need to adjust the display through the option in the ZOOM screen.
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