Question

Geometry help. Pleas
Questions are in comment

Answer 1

1) \(f: \mathbb R \rightarrow \mathbb R : f(x) = \dfrac{x-1}{3}\) is it a transformations of the plane?

Answer 2

2) \(f: \mathbb R \rightarrow \mathbb R : f(x) = x^2\) is it a transformations of the plane?

Answer 3

3) \(f:\mathbb R \rightarrow \mathbb R: f(x) = sin x\) same question

Answer 4

4) \(f: \mathbb R \times \mathbb R \rightarrow \mathbb R \times \mathbb R : f(x,y) = (2x, 3y)\) same question

Answer 5

Much luck I wish I knew how to help :(

Answer 6

5) \(f: \mathbb N\times \mathbb N\rightarrow \mathbb N\times \mathbb N : f(x,y) = (2x, 3y)\) same question

Answer 7

@FibonacciChick666 this geometry problem kills me. hehehe

Answer 8

@zepdrix

Answer 9

ok, maybe I've done this. Can you explain what "is it a transformations of the plane? " means?

Answer 10

does that mean you can still map to every point in the plane?

Answer 11

Definition: A transformation of the plane, t, is a one to one mapping of points of the plane onto points in the plane.

Answer 12

ok, so, essentially what I'm getting is we want to know if it is bijective?

Answer 13

Why don't they call it as bijective? It makes the life easier. The way they interpret the "transformation" is ambiguous to me.

Answer 14

2) and 3) are not one to one for sure, hence rejected, right?

Answer 15

well, I assume because there are different types of transformations and they existed prior to abstract algebra? I don't really know. But honestly, to me, it means that the function has an inverse whose range fully spans the original domain

Answer 16

That's what I think. But please get a second opinion. I don't trust myself.

Answer 17

5) is not onto, but it is one to one. then??

Answer 18

OMG, where are highschool students???

Answer 19

well we would need a y value of 1/3 y for every y to exist

Answer 20

lol why?

Answer 21

because it is a highschool stuff

Answer 22

For 5) if (1,1) is in the range, then there is no its preimage in domain. Hence it is not onto

Answer 23

this is not high school stuff. I didn't touch this crap till junior year college

Answer 24

and yep, good counter ex for 5

Answer 25

Actually, it is the course for highschool teacher, right?

Answer 26

no, just a general math degree

Answer 27

high school teacher classes are wayyyyyyyyyyyyy easier

Answer 28

due to the lack of having to prove anything

Answer 29

but we study this stuff to teach highschool students, So I assume that highschool students know it.

Answer 30

haha, no. I had geometry in ninth grade. I NEVER even learned about planes bigger than the "x,y plane" and they never called them real, integers, natural, etc planes

Answer 31

Also, I got a job!!