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\usepackage{tikz}
\usepackage{pgfplot}
Graphing in LATEX.
In this section we will take a look at how to draw graph
in Latex. this can be easily made in Latex, it's simple, fast, and the result
is compact and clean. To draw a graph we will need to use two packages: TikZ and PGF,
so before starting don't forget to add them to the Latex document.
To add the packages write the following line before the start of the document
Drawing a Cartesian plane.
For drawing a Cartesian plane we need firs to create the environment
for the code. ...
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We can customize the axis by adding commands between the parentesis:
[option1, option2, option3,...]. We can choose the maximum and the minimal value to
be displayed in the x and y axis, we can also choose where to place ticks marks. Using
the commands: xmax=value ,xmin=value we can set the x axis, with ymax and ymax we set the
y axis. With only those commands it will be displayed a empty rectangle, to put the x and y
axis in the middle we ca use: axis x line=middle, axis y line=middle in the option parentesis.
For example if we want to display a cartesian plane where the axis x and y
go from -5 to 5 we can write:
\begin{tikzpicture}
\begin{axis}[option of the axis]
...
\end{axis}
\end{tikzpicture}
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\begin{tikzpicture}
\begin{axis}[xmin=-5, xmax=5, ymin=-5, ymax=5, axis x line=middle, axis y line=middle]
\end{axis}
\end{tikzpicture}
Adding equation.
After setting the Cartesian plane we can add a function, Latex
will draw it automaticaly on the plane, to add an equation we simply add the
command line: \addplot[option]{function}.
Inside the [option] parentesis we can choose the domain of the function: [domain=-4:5],
now the domain will go from -4 to 5. If we want to display the graph of the function
F(x)=2x+2 we simply use the following code:
We can also add more than one function in a single graph, to do this we just add another
\addplot[]{}; in the same environment. When adding multiple function in a graph is better
to distinguish them, Latex allow us to choose a color for each function. Now we will add
two more function, one with a red line and one with a blue line:
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\begin{tikzpicture}
\begin{axis}[xmin=-5, xmax=5, ymin=-5, ymax=5, axis x line=middle, axis y line=middle]
\addplot[domain=-5:5]{2*x+2};
\end{axis}
\end{tikzpicture}
We can also add more than one function in a single graph, to do this we just add another
\addplot[]{}; in the same environment. When adding multiple function in a graph is better
to distinguish them, Latex allow us to choose a color for each function. Now we will add
two more function, one with a red line and one with a blue line:
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\begin{tikzpicture}
\begin{axis}[xmin=-5, xmax=5, ymin=-5, ymax=5, axis x line=middle, axis y line=middle]
\addplot[domain=-5:5]{2*x+2};
\addplot[domain=-5:5, color=red]{2*x+2};
\addplot[domain=-5:5, color=blue]{2*x+2};
\end{axis}
\end{tikzpicture}
Adding points.
In the plane we can also add points by simply choosing the style
and the coordinates of each point, we use the code: \addplot[option]coordinates {(2,3)};
To draw multiples dot connected by a line write: \addplot[mark=*]{(1,2)(3,4)(-2,5)}; Instead
if we want multiple dots not connected between them, we have to make a \addplot[]{} for each
point.So if we want to add four dot in the intersection of our function the code will
be:
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\begin{tikzpicture}
\begin{axis}[xmin=-5, xmax=5, ymin=-5, ymax=5, axis x line=middle, axis y line=middle]
\addplot[domain=-5:5]{2*x+2};
\addplot[domain=-5:5, color=red]{2*x+2};
\addplot[domain=-5:5, color=blue]{2*x+2};
\addplot[matk=*] coordinates {(2,2)};
\addplot[matk=*] coordinates {(0,0)};
\addplot[matk=*] coordinates {(-2,-2)};
\addplot[matk=*] coordinates {(0,2)};
\end{axis}
\end{tikzpicture}
Adding text.
We can even add a title to our graph, we just need to
add: [title=Title goes here] after the: \begin{axis}. the code will look
like this:
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\begin{tikzpicture}
\begin{axis}[title=Here goes the title]
\addplot[domain=0:5]{x+2};
\end{axis}
\end{tikzpicture}
Exercise.
Now that you know the basic try to draw the function: F(x)=x^2 -4 and put 2 dot where the function intersect with the x axis. For the solution move the mouse over the black box on the right side.
\begin{tikzpicture}
\begin{axis}[xmax=5, xmin=-5, ymax=5, ymin=-5, axis x line=middle, axis y line=middle]
\addplot[domain=-5:5]{x^2-4};
\addplot[mark=*] coordinates {(-2,0)};
\addplot[mark=*] coordinates {(2,0)};
\end{axis}
\end{tikzpicture}