Table of a calculator Vocabulary : graphing calculator – to evaluate a function at

x=... - Home screen – function editor - key -

to input an expression - table of values – variable – column – cursor -

There are many different ways to evaluate a function with a graphing calculator. Let's use the function f  x =3x 2−5x2 and evaluate this function at x=4.5 .

2 3×4.5 −5×4.52 .

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We can do this on the Home screen by calculating

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The best way to evaluate a function makes use of the function editor, which is accessed by pressing the Y= key.

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You can enter up to ten functions at a time on the TI-82 stat. Each function has its own "name", called Y1, Y2, etc. If your Y= screen is not blank, clear your function editor at this point. To enter your function, decide which of the ten function "names" you would like to use and input the expression for your function to the right of its equal sign. Let's enter the function under the "name" of Y3. Notice that we only need to enter the right side of this equation.

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The table can be used to evaluate a function more than once or twice. To use the table the function must be defined in the Y= editor (which we have already done). To access the table setup screen, press 2nd TBLSET. This screen gives you the opportunity to decide how you want the table to work. * If you want the freedom to enter any values of x, one at a time, then you can ignore the first two settings and will want ASK highlighted for the independent variable (Indpnt:). * If AUTO is highlighted for the independent variable, then the TI-82 stat will generate a whole table of values all at once based on the first two settings. For most situations you will always want the dependent variable (Depend:) set to AUTO.

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Let's use the table to evaluate the function we defined as Y3 for x = 4.5 and x = -9/7. Set the independent variable to ASK, then access the table itself by pressing 2nd TABLE. Notice the two columns; the second column is titled Y3 because that is where we defined our function in the Y= editor. Enter the values for x one at a time. As each x-value is entered the corresponding y-value will appear in the Y3 column. Notice that both the last x and Y3 value are rounded off in the table. To see the complete value, position the cursor over each one and the full value will appear at the bottom of the screen. In general, the numbers that appear in the table will be affected by the current mode settings, although positioning the cursor over any value will always reveal its full decimal equivalent.

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If you move the cursor to the top of the Y3 column, the equation that we used to define Y3 in the Y= editor will appear at the bottom of the screen. This is convenient if you have forgotten what the equation was.

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Now let's use the table to evaluate the function Y3 for x-values spaced two units apart, starting at x = -4. Return to the table setup screen. TblStart is the value of x that you would like the table to begin at, and ∆Tbl is the spacing between x-values. We also want to change the independent variable setting to Auto. Return to the table, and the TI-82 stat will evaluate the function Y3 for each x-value automatically. With the independent variable set to Auto, you can scroll up or down in the table to evaluate the function at additional values of x. The x-values will maintain a spacing of 2 units. To scroll, the cursor must be in the X column. Just press the up arrow or down arrow repeatedly.

Exercise 1: Check your results of your homework.

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a x =2x −10x25 for x betwwen 0 and 5.

Use the table to evaluate the function a for x-values spaced 0.5 units apart, starting at x = 0, ending at x = 5. Exercise 2: If

f  x =

x2 , then calculate (if possible) the image of all integers from -5 to 5, and check your 1 x

results with your calculator .