Athanasios Paraskevopoulos
Plotting basics encompass understanding and creating visual representations of mathematical functions. Essential functions include linear, quadratic, cubic, exponential, logarithmic, and trigonometric. Accurate plotting helps visually interpret relationships, trends, and predictions.

Introduction

In this project, we will explore the fundamentals of plotting basic functions. This includes understanding the nature and types of these functions, such as linear, quadratic, exponential, and trigonometric, and visually representing them in a graphical form. The project will allow us to delve into the relationships between inputs and outputs, as well as the importance of selecting suitable scales for the axes. Through this, we’ll develop a solid foundation in mathematical graphing, a skill integral to many fields such as physics, engineering, economics, and data analysis. Let’s dive into the fascinating world of functions and their graphical representations.

Plotting Functions

In[]:=
Plot[Sin[x],{x,0,2Pi}]
Out[]=
In[]:=
Plot[{Sin[x],Sin[2x],Sin[3x]},{x,0,2Pi},PlotLegends->Placed["Expressions",Below]]
Out[]=
sin(x)
sin(2x)
sin(3x)
In[]:=
Plot[{Sin[x],Cos[x]},{x,0,2Pi},PlotLabels->"Expressions"]
Out[]=

Filling between two curves

Let’s plot “
3sinx+x
” where
x
is in range of 0 to 7 and filling the bottom
In[]:=
Plot[3Sin[x]+x,{x,0,7},Filling->Bottom]
Out[]=
Plotting and filling between the curves
sinx
and
x
, where
x
is in range of 0 to 10
In[]:=
Plot[{3Sin[x],x},{x,0,10},Filling->{1->{2}}]
Out[]=
Plot the function
sin(30sin(x))
, where
x
is in range of 0 to 5
In[]:=
Plot[Sin[30Sin[x]],{x,0,5},Filling->Axis]
Out[]=
Plotthefunction
1
x
,where
x
isinrangeof-1to1
In[]:=
Plot[1/x,{x,-1,1},Filling->Top]
Out[]=

Drawing curves where function ranges becomes non reals, discontinuous and use of exclusion

In[]:=
Plot[Sqrt[x],{x,-5,5}]
Out[]=
In[]:=
Plot[Floor[Sqrt[x]],{x,0,100}]
Out[]=
The Exclusions option in the Plot function is used to specify where Mathematica should leave breaks in the plot. This is typically useful when dealing with functions that have discontinuities, singularities, or other points where the function does not provide a real - valued output .
In this case, Mathematica will not exclude any points, and the plot may have a vertical asymptote

Labelling and Legending Curves

References

◼
  • Wolfram Mathematica Documentation Center - Plotting Guide:
    ​https://reference.wolfram.com/language/guide/PlottingAndGraphics.html
    • ◼
  • Wolfram Language & System Documentation Center - Plot function:
    ​https://reference.wolfram.com/language/ref/Plot.html
    • ◼
  • Wolfram Alpha Blog - Advanced Plotting with Mathematica:
    ​http://blog.wolframalpha.com/2011/06/28/advanced-plotting-with-mathematica/
    • ◼
  • Trott, M. (2004). The Mathematica GuideBook for Graphics. Springer-Verlag New York.