Plotting a function that has a discontinuity

Example #1 .

Let’s plot the function . This function has a break at a dot . These points are vertical asymptotes and need to be plotted.

Graphs of the asymptote function: and .

Plotting a Function is feasible on the intervals [-10;-2,2] and [-2,1;2,1] and [2,2;10] with a step of 0.2.

The construction process (Figure 15 shows the entire result of obtaining data series for plotting the function and asymptotes):

1. In cell B2, enter the step of changing the argument of the function y(x).

2. Enter the initial value of the argument in cell A5.

3. In cell A6, enter the filling rule – the formula =A5+$B$2.

4. Let’s use the autocomplete function and get the argument change from -10 to 10.

5. In cell B5, enter the formula for calculating the function: =A5/((A5^2)-5) and use the autocomplete function up to cell B105.

6. In cells C5 and D5, we will enter the formulas for the asymptotes and also use the autocomplete function.

Figure 15

Based on the data obtained, we construct a graph of the function for three ranges of the argument and two graphs of vertical asymptotes:

1. Select the chart type – ” Scatter with smooth curves and markers ” (see Figure).

2. Right-click on an empty chart and select “Select data”.

3. In the “Select data source” window, use the “Add” button. As a result, the “Change Series” window will open (Figure ), in which you must specify the data for the functions when the argument changes from -10 to 2.3:

a. In the first line specify the name of the first row by clicking on the button ,

b. click on the name of the series, i.e. by cell B4 or enter the absolute reference =Sheet1!$B$4 into the “Change Row” window,

c. Click on the button , the row name will be displayed to the right of the button ,

d. In the second line specify the argument values by clicking on the button and highlighting the range A5-A43,

e. Click on the button , the row values will be displayed to the right of the button ,

f. In the third line specify the value of the function (preliminarily removing all the symbols contained in it) by pressing the button and highlighting the range B5-B43,

g. Click on the button , the function values will be displayed to the right of the button ,

h. Complete the data entry by clicking on the “OK” button.

4. To add the values of the function graph on the graph when the argument changes in the intervals [-2.2;2.2] and [2.2;10], as well as vertical asymptotes, use the “Add” button in the “Select data source” window.

5. Change the name of the graph, the name of the axes, the maximum and minimum values of the abscissa axis and the y-axis.

6. The result is shown in Figure 18.

Figure 16

Figure 17

Figure 18

Tasks №2,3

Using the Microsoft Excel package, construct a graph of the functions given in Appendix 3.4, according to the option. The calculation procedure and the result should be presented in the form of a report containing the following items:

a. First sheet: Title page – see Appendix 7 for an example of design,

b. Give the text of the task,

c. Conduct a function study that includes

i. Domain of definition of a function, selection of special breakpoints,

ii. Checking for vertical asymptotes at breakpoints and at the boundaries of the domain of definition,

iii. Finding points of intersection with coordinate axes,

iv. Set is a function of even or odd[3],

v. Set whether a function is periodic or not[4] (for a trigonometric function),

vi. Find extremum points and intervals of monotonicity (decreasing and increasing functions),

vii. Find inflection points and intervals of convexity and concavity, find oblique asymptotes of a function,

d. Plot the function and asymptotes, if any.

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