Introduction to Functions

• THIS IS A SET OF DISTINCT ORDERED PAIRS (X, Y) FOLLOWING A CERTAIN RULE SUCH THAT EVERY ELEMENT IN THE DOMAIN IS PAIRED AT LEAST ONCE WITH THE ELEMENTS IN THE RANGE.

  Relation
• The first component in the ordered pair is the x-coordinate or the abscissa while the second component is the y-coordinate or the ordinate
• The set of all possible x-coordinates is called the domain
• The set of all possible y-coordinates is called the range
• T Y P E S O F RELATION

  One-to-One Relation

  One-to-Many Relation

  Many-to-One Relation
• A function is a relation whose first element 𝑥 in the set of distinct ordered pairs ( 𝑥, 𝑦 ) is paired exactly once with 𝑦.
• Ways of Expressing Relations and Functions:

  By set of ordered pairs

  By table of values

  By graph

  By equation

  By array or mapping
• Identify the following whether a function or a mere relation:

  1.ONE-TO-ONE RELATION

  2.ONE-TO-MANY RELATION

  3.MANY-TO-ONE RELATION

  Function

  Mere Relation

  Function
• What Way of Expressing Relations and Functions is this?

  (2,3) , (−1,0) , (5,1) , (18,−2)

  By set of ordered pairs
• Identify the following whether a function or a mere relation:

  Function

  
• Identify the following whether a function or a mere relation:

  Mere Relation

  
• Identify the following whether a function or a mere relation:

  Function

  
• Fill in the blanks:

  One

  
• Identify the following whether a function or a mere relation:

  Function

  
• Identify the following whether a function or a mere relation:

  Mere Relation

  
• Identify the following whether a function or a mere relation:

  Function

  
• Identify the following whether a function or a mere relation:

  Mere Relation

  
• Identify the following whether a function or a mere relation:

  Mere Relation

  
• Identify the Way of Expressing Relations and Functions:

  By table of values

  
• Identify the Way of Expressing Relations and Functions:

  By Array or Mapping

  
• Identify the following whether a function or a mere relation:

  1.Mere Relation

  2.Function

  3.Function

  4.Mere Relation

  
• Identify the following whether a function or a mere relation:

  1.Function

  2.Mere Relation

  3.Function

  4.Mere Relation

  5.Mere Relation

  
• Identify the following whether a function or a mere relation:

  1.Function

  2.Mere Relation

  3.Function

  4.Mere Relation

  5.Function

  
• Identify the following whether a function or a mere relation:

  Function

  
• Identify the following whether a function or a mere relation:

  Mere Relation

  
• In a graph if there is only one point of intersection then it is a function
• If y is raised to an odd number then it is a function