You are Here: Home >< Maths

# Mapping and functions watch

1. Consider a rule that maps set A to set B in a one-to-one mapping. However it does not map every element of A. Is it a function?

Also if a mapping has several rules for several conditions and it happens that the graph is not continuous (such as f(x)=x^2 for 0< x < 3, f(x)= 10x for x>=3) is it a function?
2. All elements from set A have to be mapped to set B to be a function. What's more, an element in A can only be mapped to one element in B but every element in B need not be mapped to from A.
3. (Original post by Rana1997)
Consider a rule that maps set A to set B in a one-to-one mapping. However it does not map every element of A. Is it a function?
Every element of the domain must be mapped for it to be a function.

Also if a mapping has several rules for several conditions and it happens that the graph is not continuous (such as f(x)=x^2 for 0< x < 3, f(x)= 10x for x>=3) is it a function?
Functions can be continuous and discontinuous. 3 is mapped so that is a function with domain x>0.
4. (Original post by Rana1997)
Consider a rule that maps set A to set B in a one-to-one mapping. However it does not map every element of A. Is it a function?

Also if a mapping has several rules for several conditions and it happens that the graph is not continuous (such as f(x)=x^2 for 0< x < 3, f(x)= 10x for x>=3) is it a function?
All because the graph is discontinuous doesn't mean the mapping cannot be a function. You can have functions that are discrete. There's is a notion that functions can be either continuous or discontinuous.
The function is a function though not continuous.

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: October 24, 2016
The home of Results and Clearing

### 3,403

people online now

### 1,567,000

students helped last year
Today on TSR

Hang on, have Edexcel's come out already?

### University open days

1. SAE Institute
Animation, Audio, Film, Games, Music, Business, Web Further education
Thu, 16 Aug '18
2. Bournemouth University
Fri, 17 Aug '18
3. University of Bolton
Fri, 17 Aug '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams