Thread: Bijections

how do you tell if a function is a bijection? can someone please give me an example?

defined by . Show that it is injective and surjective.

sorry i mean like when you are given the function like 3x-2 and you need to see if it is a bijection? i know the definitions that i needs to be one to one and onto. i am just wondering how do you tell this from the function? do you graph it or i mean i dunno im so confused!

Originally Posted by srw899

sorry i mean like when you are given the function like 3x-2 and you need to see if it is a bijection? i know the definitions that i needs to be one to one and onto. i am just wondering how do you tell this from the function? do you graph it or i mean i dunno im so confused!

You can tell by the graph. It passes the horizontal line test.

im sorry but i forget, how do you do the horozontal line test? (*im sorry if i seem dumb, and thank you so much for your help, i really appreciate it*)

alright ive got it, thanks so much!!! wow i feel befuddled! for others:

horozontal line test is when you graph the function and draw a horozontal line, if it crosses the function more than once then once the function is not one to one.

bijections are true both ways.

if a bijection is true, then the converse of the bijection is true.

other than graphically, you can show a function is a bijection if it is one-to-one and onto, that is, it is both injective and surjective. a quick wiki or google search can show you what these are