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How to how to create a table of function values. (And introduction to functions)

 This topic is part of the TCS FREE high school mathematics 'How-to Library'. It introduces the concept of a function, and shows you how to create a table of function values. (See the index page for a list of all available topics in the library.) To make best use of this topic, you need to download the Maths Helper Plus software. Click here for instructions.

### Theory:

A function is a set of ordered pairs where for any 'x' value in the set, there is only one 'y' value.

For example, this set of ordered pairs is a function: { (0,0) (1,1) (2,8) (3,27) }

A rule that generates the entire set is written as: 'y = f(x)', which is short for: 'y is a function of x'.

The rule: y = x³ generates the set of ordered pairs above, plus an infinite number of other ordered pairs. It is a function because for every 'x' value, there is only one possible 'y' value:

These results can be displayed in a table, like this:

 x y = f(x) 0 0³ = 0 1 1³ = 1 2 2³ = 8 3 3³ = 27

For more complicated functions, such as: y = 2x² - 5x + 2, a table of values will help you to evaluate and graph the function.

### Method:

Maths Helper Plus makes it easy to prepare a table of function values. As an example, we will show you how to create a table of function values for y = 2x² - 5x + 2. The table will also include separate columns for each of the three terms.

If you have just launched the software then you already have an empty document, otherwise hold down ‘Ctrl’ while you briefly press the ‘N’ key.

#### Step 2  Enter a function: y = f(x)

1. Press the F3 key to activate the 'input box' for typing (see below):

2. Type your function, as shown below:

3. Press Enter to complete the entry

#### [Optional] Adjust the graph scale and position

Only if you wish to view the graph of your function, you may need to adjust the scale settings in order to see the interesting parts of the graph.

If the graph does not display at all, or not enough of it can be seen, reduce the scale by pressing the F10 key briefly. Repeat until the graph is visible. To enlarge the graph if it is too small, hold down 'Ctrl' while you press F10.

To view different parts of the graph without enlarging or reducing, hold down both 'Ctrl' and 'Shift' while you press any of the keyboard arrow keys.

#### Step 3  Create the table of function values

1. Carefully double click beside the function edit box on the text view.

The correct place to double click is shown by the red rectangle in the diagram below:

This will display the 'options dialog' for your function.

2. Click the 'Data Table' tab at the top of the options dialog. The options box 'Data Table' tab will display as shown below:

3. Enter 'x' values for your data table. To do this you click inside the top edit box, and type the 'x' values separated by commas:

-1, -0.5 , 0, 0.5, 1, 1.5, 2, 2.5, 3

HINT: For evenly spaced 'x' values, you can use the 'series operator'.

For this example, you can enter the same values as listed above like this:  <-1, 3, 0.5> This means: 'x values from -1 to 3 in steps of 0.5. For more information on the series operator, see the Maths Helper Plus 'Help'.

4. Enter expressions for your data table. These will be evaluated for each 'x' value you typed in the top edit box.

To do this you click inside the bottom edit box, and type the expressions separated by commas.

HINT: For the simplest table, the only expression needed is: 'y'.

To see how a complicated function can be evaluated, include some simpler expressions that form the function.

For example, for the function: y = 2x² - 5x + 2 , these expressions may be useful:

x², 2x², -5x, 2, y

(Separate the expressions with commas.)

5. View the table. Click the 'OK' button at the bottom of the Options dialog box. The text view will now display the table of values. (See below:)

HINT: If you can only see part of the table, hold down Ctrl and press the 'T' key to display text only. To return to displaying both graph and text, hold down Ctrl and press the 'B' key.

 x       x²      2x²      -5x       2       y  -1      1       2        5         2       9  -0.5    0.25    0.5      2.5       2       5  0       0       0        0         2       2  0.5     0.25    0.5      -2.5      2       0  1       1       2        -5        2       -1  1.5     2.25    4.5      -7.5      2       -1  2       4       8        -10       2       0  2.5     6.25    12.5     -12.5     2       2  3       9       18       -15       2       5

6. To change the settings for your table, double click on the text view to the left of the table, anywhere on the area shown by the red box in the diagram below:

The data table tab of the options dialog box will display immediately so that you can edit the values.