Functions and Mappings

Okay, so this year I'm going to be teaching myself all of A2 maths. I started today and I'm already struggling with functions and mappings. What on earth is a mapping?! I'm seeing things saying are 1-2-1 mapping and I just having a clue what it is on about!! What does a mapping represent?

Thank you in advance for any help I get

Charlotte

Reply 1

username1560589

A mapping is the same as a function. If you haven't come across the term yet, an inverse function is one that undoes a particular function. eg y = x + 1 is the inverse of y = x - 1. If you apply both in succession, you get back what you started with.
In a 1 to 1 mapping, each possible value of x maps to a single value of y and each possible value of y maps to a single value of x. The function has an inverse. eg y=x

In a many to 1 mapping, each possible value of x maps to a single value of y but a value of y might not map back to a single value of x. The function does not have an inverse function, but you can restrict the domain of the inverse to make it a function. eg

y = x^2

There is another relationship called 1 to many where each possible value of y maps to a single value of x but a value of x might not map back to a single value of y. This is not a function, but its inverse is. eg

x = y^2

Reply 2

B_9710

For a function to be a function, one element from the domain can be paired to ONLY ONE element from the range meaning that for any x value you put into the function, you can only get one value that comes out. So x=y^2 is not a function for example as for say x=4 y could be 2 but equally it could be -2. A 1-2-1 function ( one to one) means that there is only one x value that corresponds to only one y value. All linear graphs are 1-2-1 A many to one function means that there is more than one x value for a particular y value. An example of this is f(x) = sinx
There are infinitely many x values that correspond to sinx = 1. But for each x value you still only get one value for f(x) or y if you will. y and f(x) essentially mean the same thing