A function is a relation in which each member of the domain (this is the set of x values) is mapped to only one member of the range (this is the set of y values), that is, a one to one mapping. A function is also defined in terms of a many to one mapping; this is where more than one x values in a domain are mapped to only one y value in a range.
Example of a One to One mapping
Using the equation, f(x) =5x + 2
Where, f(x) means ‘the function of x is 5x + 2’
And, y = f(x).
Recall the y values are obtained by substituting the domain values for x in the equation.
That is, when x = 1
y = 5(1) + 2
y = 7
Example of a Many to One mapping
Using the equation, f(x) = 2x2 + 3x – 2
Note: The x values are obtained by substituting the y values in the equation for f(x), that is, when y= -1, x= -1.78 or 0.28.