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Functions & Relations Catalogue

 

What is the difference between a function function and simply a relation?

See here why the circle is not a function.

Functions vs. Relations

 

 A fun way to learn about functions.
Try the FLASH CARDS, identify functions visually

 

Shortcuts

Constant Hyperbola Gaussian Functions
Linear Polynomial Ratio Functions Hill Equation    
  Polynomial Functions Lorentzian Function    
Log and Exponential
 

 

Visual Function Map


  





 



 
   
     

  

 

 

 

(click on the graph to manipulate k)

Constant Click on the graph to change the constant.
   
Linear Click on the graph to change the line parameters y = mx + b.
   
Hyperbola
 


Gaussian Function       The (visual) difference between the Gaussian and Lorentzian functions.
(see Lorentzian section)

Gauss and Lorentz lineshapes.png
By Petergans - Using EXCEL Previously published: none, Public Domain, Link
       
   
Polynomial Ratio Functions
 
Polynomial functions Notice the number of changes in direction correspond to the highest exponent of this function (in this example it is 5).  
  Click on the graph below to change the parameters.
   
Log and Exponential Click on the graph below to change the parameters.
Notice which are the counter parts: (i) red and blue, and (ii) green and orange.
   
Hill Equation
 



Lorentzian Function

Read more about the
Click on the graph below to change the parameters.

 The (visual) difference between the Gaussian and Lorentzian functions.
(see Gaussian section)

Gauss and Lorentz lineshapes.png
By Petergans - Using EXCEL Previously published: none, Public Domain, Link
   
   

 

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