Two and three dimensional plotting with 'Octave'

Greetings, in this tutorial we will deeply focus on plotting a function on Octave. To have a background information or if you're wondering what is Octave, i strongly recommend to take a look at my introduction to Octave tutorial. To plot a function in two dimensional cartesian coordinate system we need two variables and an equation showing how dependent these two variables are. To denote these two variables similar to axes, 'x' and 'y' letters will be used.Below are some primitive simple equations that can even be plotted by hand with some basic math,

Above equations are relatively easy to draw by hand after finding critical points and by simply plugging some sample x values to observe the behaviour of y. However not every function is as easy as the above ones. Some functions require more effort and computation to plot by hand. In these circumstances it's much more efficient to use a software capable of plotting & calculating complex functions. Below are some examples of such functions,

As you can see above functions are quite time consuming to solve by hand. Thereby we will use the plot function of Octave to witness their behaviour.
The very first thing we need to do is to define the range of x so that our graph will picture that interval.
To do that we can write the below code on Octave's command window,

X = -10:0.1:10

Which will give us a 1x201 matrix consisting of rational numbers from -10 to 10 with an increase of .1
So it will go like, -10, -9.9, -9.8, -9.7, .... 9.7, 9.8, 9.9, 10.

Then simply define y according to x. I will first do it for the x+10 example,

y = X + 10

Which is simply adding ten to all x values,

And then to plot simply wrote the code below,

plot (X,y)

and here is your graph,

To proceed this time we will do it for relatively complex functions, First one will sin and cos function,

x = x=0:pi/10:2*pi;
y=sin(x);
plot(x,y)

Then as a second task we can label x and y axes and name our plot with the following code,

xlabel('X');
ylabel('Y');
title('sin plot');

and to add cos function to the same ploot and change the color of sin function to red, cos to blue we can write the below code,

x = x=0:pi/10:2*pi;
y=sin(x);
plot(x,y)
xlabel('X');
ylabel('Y');
title('sin plot');
y1 = cos(x);
plot (x,y,'r');
hold on;
plot (x,y1,'b');

Briefly in the above plot the blue wave shows cos and red sin function in the interval of 0 to 2*pi or 360 degrees. To draw a graph on logarithmic scale, Meaning the y axes will be marked acording to the powers of ten. Mostly used when there is a large number of quantity. Lets draw 2^x and x^x+10 on logarithmic scale,