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# UNIT 4 CALC. ACTIVITY 7

UNITAT 3. M2P5

ACTIVITY 7.

Graphic study of mathematical functions

### ACTIVITY 7.1 The second degree function f(x)=Ax²+Bx+C

• .Open the L.O.Calc. Open your student template . Open the sheet 7.1 Estudi gràfic de funcions matemàtiques. We are going to make a chart representing the function f (x) = Ax² + Bx + C.

• Align to the center the columns B and C

• Merge the cells B2, and C2. Write in B2:C2 the title of the chart:f Funció f (x) = Ax² + Bx + C . Set a size of letter of 16 points and bold letters

• Merge the cells B3, and C3. Write in B3:C3 the text taula de dades.

• Type X in B4 and f(X) in C4 and in two contiguous cells leaving row 1 blank

• Highlight B4:C4 setting a background color

• Fill the X column (column B) with values ​​from -10 to 10 with in intervals of 0.5 (in total you have to fill 41 cells). You aren't supposed to type the values. Create a series:​​.

• Select the 41 cells starting with B5 to B46

• Use Edita | Emplena | Sèries, set an Initial value of -10 and an Increase of 0.5

• Prepare in E4:G5 the the table of coefficients A, B and C as shown in the image below.

• Define the following data areas:

• Select the 41 cells where you have written the values ​of X (B5:B45) and, with Ctrl + F3, define the data area as X

• Define E5 using Ctrl + F3 as A. F5 must be named and B. G5 must be called C
The sheet must look like the one shown below

•

• Calculate the function values

• Place the cursor in C5 and write the formula = A * X ^ 2 + B * X + C. Keep in mind that X, A, B and C refer to the data areas that you have defined before, and Calc will replace them with their corresponding reference.

• Extend C5 to C46

Save the document using the save button or Archivo | guardar. Never use Save as (archivo |  guardar como ) otherwise the previous versions in your document will be lost. Save a version and call it 7.1.1

Make the chart

• Select the data ​​table (B4: C45)

• Click on the tool Insereix un diagrama. This will start the Charts Wizard

• In the first step, choose the the type of chart XY (dispersió) with the Només línies variant. Click the Properties button and mark the B-Spiline option and click OK. Then click Nex

• In the second step, Interval de dades, make sure that the only box selected is La primera fila com a etiqueta and press the Next button

• In the third step,Sèrie de dades, do not modify anything and press Next
In the fourth step,
Elements del diagrama, write the title of the diagram: Funció de segon grau and click on finalitza.

Save the document using the save button or Archivo | guardar. Never use Save as (archivo |  guardar como ) otherwise the previous versions in your document will be lost. Save a version and call it 7.1.2

Modify the look of the chart

• Double click on the chart and select the menu option Format | Àrea del diagrama, click on the àrea tab to choose the color Verde 4 (or whatever other you consider suitable) and click OK

• Select Format | Pla lateral del diagrama. In the Area tab choose the color Yellow 3 and click OK

• Select the menu option Insereix | Eixos. Check the boxes S Eix secundari X and Eix secundari Y and click OK

• Select the menu option Format | Eix | Eix Y and select the tab escala

• Disable all the boxes Automatic from the block Mida dels eixos

• Enter 100 at the Maximum Value

• Enter 25 at Main Range (Interval principal)

• Enter 25 a Number of secondary intervals (Nombre d'intervals secundari)

• Leave the other options unchanged

• Select the tab posicionament.. In the tag location field select comença fora and click OK

• Do the same in Format | Eix | Eix Y secundari axis. Place the tip of the mouse pointer over the line of the graph (the parabola). When the sign Sèrie de dades "F(X)" appears, double-click it

• On the Línia tab, change the value of amplada to 0.10cm

• Change the color of the line to Blue 1

• Click OK

• Select the menu option Insereix | Graelles

• Check the box Eix X on the Quadr. principal block and click OK

• Select the menu option Format | Graella | Totes les graelles dels eixos

• Dropdown the control Propietats de la línia / Estils and choose Traços molt fins

• Change the Transparency value to 50% and click OK

• Modify the height and width of the chart until it looks like the one shown below

Save the document using the save button or Archivo | guardar. Never use Save as (archivo |  guardar como ) otherwise the previous versions in your document will be lost. Save a version and call it 7.1.3

#### Function behaviour

Changing the values of A, B and C, we can see the different possible behavior of second degree functions.

• Notice what happens if you change all the signs of the three coefficients

• Increasing or decreasing the coefficient A

1. Setting to 0 two coefficients

MAKE A BACKUP COPY OF YOUR ACTIVITIES FILE. Open the file browser Nautilus using LLocs | inici. Open your calc activities folder. Select your Calc activities file and copy it (ctrl+c) and paste it (ctrl+v) in the same folder. This will create a perfect safety copy of your activities file, keeping in it the versions. Carry on working with the original file.

## ACTIVITY 7.2 Other mathematical functions

Take advantage of the spreadsheet to represent other types of functions. It will be necessary to vary some of the conditions of the axis scales and, of course, the formula that calculates the value of the function.

• Select the sheet 7.2

• Put the cursor over the name of the sheet, and get the contextual menu. Select the option Move / copy sheet, Set as name of the copy sin (x)

• Change the title to f (x) = sin(x)

• In B5 create a new serie

• Minimum value -1

• Maximum value 1

• Main range 0.1

• Secondary interval 0.1

• Extend to B46

• In C5 write the formula = sin(x) and extend to C46

• the scale conditions of the Y axis must be changed to

• The graph would look like this one

Save the document using the save button or Archivo | guardar. Never use Save as (archivo |  guardar como ) otherwise the previous versions in your document will be lost. Save a version and call it 7.2.1

## ACTIVITY 7.3 Napierian logarithm ln(x)

• Repeat the process to represnet the function f(x)=Ln x. First select the sheet 7.3ln(x)

• The function to insert in the column C will be =SI(x< =0;"";LN(x)). The conditional function is needed to avoid calculating the naperian logarithm of a negative number

• The range of values in aixe Y must be:

• Valor mínim -1

• Valor màxim 2,50

• Interval principal 0,5

• Interval secundari 0,5

• The chart must similar to this:

Save the document using the save button or Archivo | guardar. Never use Save as (archivo |  guardar como ) otherwise the previous versions in your document will be lost. Save a version and call it 7.2.3

## ACTIVITY 7.4, 7.5, 7.6, 7.7

To make each of these four charts, use the sheets 7.4, 7.5, 7.6, 7.7.

Save the document using the save button or Archivo | guardar. Never use Save as (archivo |  guardar como ) otherwise the previous versions in your document will be lost. Save a version after finishing each chart and call them 7.4,7.5, 7.6, 7.7.

MAKE A BACKUP COPY OF YOUR ACTIVITIES FILE. Open the file browser Nautilus using LLocs | inici. Open your calc activities folder. Select your Calc activities file and copy it (ctrl+c) and paste it (ctrl+v) in the same folder. This will create a perfect safety copy of your activities file, keeping in it the versions. Carry on working with the original file.  Don't upload it to Moodle until you end the last activity

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