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COM 1013 BUSINESS MATHEMATICS
CHAPTER 03
PART II
NON-LINEAR FUNCTIONS & APPLICATIONS



Prepared By S S

, Learning Outcomes
• This chapter introduces the several types of non-linear functions whic
frequently used in economics, management and business studies.
• At the end of this chapter you should be able to:
 Recognise the general form of the equation representing a non-lin
function as well as the main characteristics of the graph representi
the function
Plot quadratic functions.
Manipulate non-linear functions algebraically, particularly in econo
applications such as demand, supply, revenue, cost and profit
 Use exponentials and logs in a range of applications, such as
production and consumption

, Non-Linear Functions
 A non-linear function is a function that is not a linear function
Graph of a non-linear function is not a straight line
The graph of a non-linear function is a curved line which is a line whose direction
constantly changes
A non-linear function has a slope that varies between points
 Some non-linear functions:
All polynomial functions except first degree polynomial function (For example, quadra
function, cubic function, etc.)
Rational functions
Exponential functions
Logarithmic functions
Absolute value functions
 The non-linear functions commonly used in business and economics:
Quadratic function
Exponential function
Logarithmic function

, Quadratic Function
A quadratic function is a function of the form

f ( x)  ax 2  bx  c ,
where a, b, and c are constants with a  0

The graph of a quadratic function is a curve called
a parabola.
Parabolas may open upward or downward and vary in
"width" or "steepness", but they all have the same basic
"U" shape.
All parabolas are symmetric with respect to a line called
the axis of symmetry.