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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

CODE
\usepackage{tikz}
\usepackage{pgfplot}
Drawing a Cartesian plane.
For drawing a Cartesian plane we need firs to create the environment for the code. ...

CODE
\begin{tikzpicture}
\begin{axis}[option of the axis]
...
\end{axis}
\end{tikzpicture}

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:

CODE
\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:

CODE
\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:

CODE
\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:

CODE
\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:

CODE
\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}