
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/(L^{2 } + 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.




