Use the tool Input Box and click in the graphics view. You can link an input box in the graphics view to a GeoGebra object. The short command for entering the degree-symbol is If you want to use degrees, you have to add the degree-symbol when writing the function, as in:į(x)=sin(x° ). The unit on the \(x\)-axis by right-clicking on the graphics view and pick Graphics. If you want to use radians, you can change When you enter trigonometric functions, the default unit is radians. Using the function inspector, you can inspect a function in an interval Using the tool Function Inspector, you can inspect a function. If you want another ratio, right click anywhere in the drawing pad where there If you want to reset the ratio between the axes to 1:1, click You can also scale the axes by using the tool Move Graphics View and then drag the axes. When the cursor changes its appearance, you can drag that axis by holding down the left mouse button and The easiest way to scale the axes is to hold down Shift and hover the mouse over one Once the concept of coefficient is understood, sliders can be used for all functions. When the students understand the concepts slope and \(y\)-intercept, you can introduce the sliders \(m\) and \(c\) to study a general linear function. For absolute beginners, it may be a good idea to start by using examples where the coefficients are not represented by sliders. The letters \(y\) and \(x\) denote variables, whereas the letters \(m\) and \(c\) denote fix numbers. H(x) = x^3-x^2+x-1 Coefficients represented by slidersįor students starting to studying mathematical functions, denoting coefficients by letters, may be an abstraction that is difficult to grasp. In that case, use \(f(x)\)-notation when entering the functions in the input bar, as in: f(x) = 2x-1 The commands used in calculus however, must work on objects that are functions. The distinction made by GeoGebra (between lines, conic sections and functions) does not matter as long as you don't have to do any calculus. Where the coefficients are either written as numbers or get their values from sliders. In the general case you can enter an equation Not all such curves are graphs of functions.Īs for lines, you can enter the equation x = 5 to get a vertical line, which isn't the graph of a function.Īs for conic sections, you can enter the equation for any conic section. Objects with the given names c, g, f.Ī curve defined by an equation in \(y\) and \(x\) is a more general concept than a graph of a function. All three objects are given names by GeoGebra. If you enter following functions in the input bar (one at a time): y = 2x-1Īnd then look at the algebra view, you can see that GeoGebra treats them as three different kind of objects: a line, a conic section, and a function. The \(f(x)\)-notation and equations in \(y\) and \(x\) Write f(x)= in the editing area and then choose \(f\) from the Object-menu. You can show a dynamic equation of the function by making a text object in the graphics view. You then make four sliders \(a, b, c, d\), and enter f(x)=ax^3+bx^2+cx+d Let's say you want to show a polynomial function of degree three. Using GeoGebra you can easily handle functions with coefficients. You can also name a function, for example by writing: myFunction(x) = sin(x) If you write an expression of \(x\) in the input bar, a function is created and given a name by GeoGebra. In most cases it is easy to guess how a function should be written. Remember: the graph is the drawn line or curve.There are a number of predefined functions and operators in GeoGebra that are shown on the site GeoGebra - Predefined Functions and Operators. This is usually seen as the y-value at the lowest point of the graph, and the y-value at the highest point of the graph. The range is found in a similar fashion to the domain, but instead of writing the interval as beginning at the smallest x-value and ending at the largest x-value, we write it as starting at the smallest y-value and ending at the largest y-value. The range is the set of all y-values of the function. This is usually seen as the left most point of graph and the right most point of the graph. The reason for this is that functions do not include just individual whole numbers, but all decimal values in between, so we write the interval as starting at the smallest included x-value and ending at the largest included x-value. The domain is generally written in either interval form (as is written in the applet above) or inequality form. The domain is the set of all x-values of the function.
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