Lessons 3–4 · 2 lessons · N. I. Taylaqov (general editor), A. B. Akhmedov, M. D. Pardayeva, A. A. Abdug‘aniyev, U. M. Mirsanov. Informatics and Information Technologies, Grade 10, 1st edition. “Extremum-Press”, Tashkent, 2017
4
Graphs of simple and complex functions
Textbook: pp. 12–14
GoalBuilds a table of function values and draws the graph with the smooth-line scatter chart.
New words
scatter chart: a chart whose points have numeric x and y values · tarqoq diagrammasmooth line: the points are joined by a curved line instead of straight pieces · silliq chiziqli grafikstep: the constant difference between neighbouring x values · argument qadamiradian: the unit of angle that Excel trig functions expect, 180° = π radians · radian
Explanation
To draw the graph of a function you first build a table of x values: write the starting value and a constant step, and AutoFill continues the rest. The formula for y is written once in the next row, and relative references copy it to all the x values. Select both rows, choose “Scatter” from the Charts group on the Insert tab and then the “Scatter with Smooth Lines” type: in this chart the x axis is a true numeric axis. An ordinary “Line” chart treats the x values as text labels and spaces them evenly, so if the steps are unequal the graph is distorted. The chart title and the axis titles are added through the chart elements. If you write the coefficients in separate cells and join them with absolute references, the graph is redrawn at once when you change them. In Excel SIN, COS and TAN expect the angle in radians, so convert degrees with RADIANS().
Worked examples
y = x² – 4x + 3, x from –1 to 5, step 1. If B2 gets =A2^2-4*A2+3, the y values are 8, 3, 0, –1, 0, 3, 8. The graph is a parabola with its vertex at (2; –1), crossing the x axis at 1 and 3.
y = sin x, x from 0 to 6, step 0.5: the formula is =SIN(A2). At x = 3 y ≈ 0.1411 and at x = 3.5 y ≈ –0.3508; because the sign changes, the graph crosses the x axis between 3 and 3.5 (at π ≈ 3.14).
Class activity
“Guess the graph”: the teacher shows only three points of y = x² – 4x + 3; pairs calculate the other points in their notebooks and then compare them with the graph drawn in Excel.
Practice
1
What is the value of y = x² – 4x + 3 at x = 5?
8
2
Which chart type suits drawing the graph of a function?
Scatter with Smooth Lines
3
How do you write the sine of 30° in Excel, and what is the result?
=SIN(RADIANS(30)); 0.5
4
Why does a “Line” chart distort the graph when the x step is unequal?
It takes the x values as text labels and spaces them evenly, ignoring the real distances.