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MATHEMATICS - CASE STUDY

    Introduction



Atom and electrons

 

The force that holds the atoms together is determined by the distance between the atoms and the number of the electrons around it. In order to better understand how the electron number and the distance affect the force, a function can be used.

What is known:

  • The force, f, is defined by the number of electrons, c, and the distance between atoms, L. The expression is
          f(L) = 2/(L2 + 2L + c)
  • A family of functions is a set of functions expressed by a formula with at least one constant. The value of the constant affects the graphic and property of the function.
  • Constant c is a positive integer.
     
    Questions

 

 

Sketch the curve of the function and show all the key features.

     
    Approach


 
  • Find the domain and the intercepts of the function.
  • Analyze the symmetry, asymptote, monotonocity, local extreme value, concavity and inflection points of the function.
  • The constant, c, affects the shape of the graphic.