Functions
Language
● Mapping = rule which associates two sets of items
● Input or Object is something which is to be mapped to something else (the
Output or Image)
● Set of possible inputs of mapping is called domain and the range is the set
of outputs for a particular set of inputs
● Four different types of mapping:
○ One-to-One → each object is mapped to exactly one image
○ One-to-Many → an object may be mapped to two or more different
images
○ Many-to-One → two or more particular
○ Many-to-Many → an object may be mapped to two or more
different images or visa versa
● Function may only have one-to-one or many-to-one mapping
The Modulus Function
● Modulus negates any negative parts of the graph and turns them positive
● I.E any negative parts are reflected in the x-axis to become positive
● Equations can be solved by taking the positive form and the negative form
of the modulus and solving them as two independent functions
● Can also be solved by squaring both sides BUT this can lead to false roots
being created, so must check all roots in original equation
Modulus Inequalities
● An inequality in the form − a < f (x) < a can be written as | f (x) | < a
● An inequality in the form f (x) < − a or f (x) > a can be written as | f (x) | > a
● The inequalities can then be solved as normal
● Often drawing the graph is useful to solve more complicated inequalities
Language
● Mapping = rule which associates two sets of items
● Input or Object is something which is to be mapped to something else (the
Output or Image)
● Set of possible inputs of mapping is called domain and the range is the set
of outputs for a particular set of inputs
● Four different types of mapping:
○ One-to-One → each object is mapped to exactly one image
○ One-to-Many → an object may be mapped to two or more different
images
○ Many-to-One → two or more particular
○ Many-to-Many → an object may be mapped to two or more
different images or visa versa
● Function may only have one-to-one or many-to-one mapping
The Modulus Function
● Modulus negates any negative parts of the graph and turns them positive
● I.E any negative parts are reflected in the x-axis to become positive
● Equations can be solved by taking the positive form and the negative form
of the modulus and solving them as two independent functions
● Can also be solved by squaring both sides BUT this can lead to false roots
being created, so must check all roots in original equation
Modulus Inequalities
● An inequality in the form − a < f (x) < a can be written as | f (x) | < a
● An inequality in the form f (x) < − a or f (x) > a can be written as | f (x) | > a
● The inequalities can then be solved as normal
● Often drawing the graph is useful to solve more complicated inequalities
