How to draw this picture with Latex?

Question

Could some one help me to draw the following picture with Latex ( using only 1 picture) ? Thank you SO MUCH for your help.

Answer 1

Here's an example of how to get started. I think it should make it clear enough how to continue to get the diagram you want.

\documentclass[border=10pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}

\begin{tikzpicture}[my midway label/.style={midway,yshift=1.5in}]

  %% case 1
  \node[anchor=east] (A/left)         at (0,0)                  {$x$};
  \node[anchor=west] (A/right)        at ($(A/left)+(1in,0)$)   {$x$};
  \node[anchor=west] (A/right/up/1)   at ($(A/right)+(0,1in)$)  {$x+dx$};
  \node[anchor=west] (A/right/down/1) at ($(A/right)+(0,-1in)$) {$x-dx$};

  \path (A/left) -- (A/right) node [my midway label] {Case 1};

  \draw[blue] (A/left) -- (A/right);
  \draw[red]  (A/left) -- (A/right/up/1.west);
  \draw[red]  (A/left) -- (A/right/down/1.west);

  %% case 2
  \node[anchor=east] (B/left)         at ($(A/right)+(1in,0)$) {$x$};
  \node[anchor=west] (B/right)        at ($(B/left)+(1in,0)$)  {$x$};

  \path (B/left) -- (B/right) node [my midway label] {Case 2};

  \draw[blue] (B/left) -- (B/right);
\end{tikzpicture}

\end{document}

There are other ways of doing this as suggested by @clement . But this approach will help familiarize yourself with some basics of TikZ.

I'll explain a few of the details here:

node syntax

\node[<optional arguments>] (<optional node name>) at (<position>) {<content>};

The one part of this syntax that you cannot omit is the content.

I use the power of the calc library to help place nodes relative to each other. That's what's happening when I write:

at ($(<previously defined node name>)+(<vector>)$)

When I opened the tikzpicture environment, I defined my own private style. This is a way of helping manage the picture. The idea is that I'm going to define a node between two points along a path and then shift it in the $y$ direction.

In this case, I used a particular instance of path syntax:

\path (<1st node name>) -- (<2nd node name>) node[<optional argument] {<content>};

Note that in this case node is not a control sequence but just a bare word.