If you enter the function \(f(x)=0.5x^2-3x+1 \) in the input bar and press enter, the graph will appear. You can drag the graph and watch how the formula for the function changes in the algebra view.
When using GeoGebra it is easy to show the graph of general functions. To make a general cubic function, like in the applet above, insert four sliders a, b, c, d and then write the function as:
If the function is called \(f\) you can use the commands
Integral[f, <Start x-value>, <End x-value>].
can be used to display the osculating circle.
If the function is a polynomial you can also use the commands
InflectionPoint[<Function>]. Note that these commands do not work if the function is entered as an
equation in \(x\) and \(y\), e.g. as
y=x^2+1. GeoGebra distinguishes between equations and functions, and
functions are written using brackets, as in \(f(x)\) or \(Malin(x)\).
Scale the axes
The easiest way to scale the axes is to hold down Shift and hover the mouse over one
of the axes. When the cursor changes its appearance, you can drag that axis by holding down the left mouse button and
drag. If you want to reset the ratio between the axes to 1:1, click
If you want another ratio, right click anywhere in the drawing pad where there
is no object and choose
In GeoGebra 4 there is a new tool called
Using the function inspector, you can inspect a function in an interval
or around a point.
Degrees and radians
When you enter trigonometric functions, the default unit is radians. If you want to use radians, you can change
the unit on the x-axis by right-clicking on the graphics view and pick
If you want to use degrees, you have to add the degree-symbol when writing the function, as in:
f(x)=sin(x° ). The short command for entering the degree-symbol is
Input Box and Composite functions
In the applet above, the Insert Input Box tool is demonstrated. In order to link an input box to a function, start by inserting a function:
Use the Insert Input Box tool and click in the graphics view, fill in caption and choose the function \(f(x)\) in the Linked Object list.
Making composite functions works as expected. The green and yellow functions in the applet above are entered as:
If you have two expressions in terms of x,
you can show for which intervals an inequality holds. As an example you can enter following
code in the input bar:
This is how you write inequalities in GeoGebra:
<, >, <=, >= stands for <, >, ≤ and ≥
Piecewise defined functions
A piecewise defined function is defined in different ways in different intervals. In GeoGebra you can
define a function on an interval by using the command
The functions above are written:
f(x)=Function[1,-10,-1] g(x)=Function[x^2,-1,1] h(x)=Function[2x-1,1,10] f_der(x)=Function[f'(x),-10,-1] g_der(x)=Function[g'(x),-1,1] h_der(x)=Function[h'(x),1,10]
There are predefined functions in GeoGebra to make Riemann sums.
- Input a function
- Insert a slider n representing the number of intervals. Make sure that the values of n are restricted to positive integers.
- Input the lower sum:
bare the endpoints of the interval.
- Input the upper sum:
- Input the trapezium sum:
- Input the integral:
Demonstrate derivative and use FormulaText
The recording below shows how to demonstrate the derivative in the same way as on the page Calculus - The Definition of the Derivative.
When displaying information about functions, you can use the text tool in the same way as with other objects. There is also a special command
which will yield the formula of a function as text. This is also shown in the recording below.
by Malin Christersson under a Creative Commons Attribution-Noncommercial-Share Alike 2.5 Sweden License