Quick Notes

Quick Notes

Mathematics Chapter 8: Graphs of Functions
8.1 Graphs of Functions
 
8.1  Functions
 
  Definition  
     
 

It is the relation in which each object in the domain has only one image in the codomain.

  
 
Identifying functions:
 

 

One-to-one functions

  
  • Relation where the object in the domain has only one image
     

Many-to-one functions

  
  • Relation where more than one object is matched to the same image
     

One-to-many relations

  
  • Relation where the object in the domain has more than one image
     

Many-to-many relations

  
  • Relation where at least one object has more than one image, and more than one object has the same image
     
Function representation:
     

 
8.2  Graphs of Functions 
 
  Definition  
     
 

Representation of a function with a straight line or curve on a Cartesian plane.

  
 
Constructing a table of values:
     
  • A table of values can be constructed to determine the corresponding value of the ordered pair \((x,y)\) before the graph is drawn.
     
Steps to draw a graph:
     
(i)   Construct a table of values for the selected range
     
(ii)   Draw and label each axis with the given scale or any suitable scale
     
(iii)   Plot the point \((x,y)\)  for the ordered pairs from the table
     
(iv)   Join the points to form a straight line or a smooth curve