# Help with vector notation

## Homework Statement

Hi. Its not really a problem but just a general question. When doing graph translations, such as move the parabola x units right or y units up etc, Is it okay to use vector format. So instead of saying move this equation 4 units left, could you write it like this -> <-4,0>

## Homework Equations

I know this is used for translations of shapes but my main question is can it also be used for graphs

## The Attempt at a Solution

I asked my teacher but he just shouted at me for asking him concepts he didnt talk about.

fresh_42
Mentor
2021 Award

## Homework Statement

Hi. Its not really a problem but just a general question. When doing graph translations, such as move the parabola x units right or y units up etc, Is it okay to use vector format. So instead of saying move this equation 4 units left, could you write it like this -> <-4,0>

## Homework Equations

I know this is used for translations of shapes but my main question is can it also be used for graphs

## The Attempt at a Solution

I asked my teacher but he just shouted at me for asking him concepts he didnt talk about.
A graph ##\mathcal{G}## of usually a function ##x \mapsto f(x)## is a set of points: ##\mathcal{G}=\{\,(x,f(x)\,|\,x \in \operatorname{domain}(f)\,\}##. This is a subset of ##\mathbb{R}^2## and to move it means to move it within this plane ##\mathbb{R}^2##. Thus you need a direction in which it is moved and a distance by which it is moved. But this exactly defines a vector ##v=(v_x,v_y)##. So the moved object will be ##v+\mathcal{G}=\{\,(x+v_x,f(x)+v_y)\,|\,x \in \operatorname{domain}(f)\,\}##. So in a sense this is even better than just to say move by ##"v_0"## in direction ##"x"## or ##"y"## since you allow more than two directions.

However, whether you should argue with your teacher is a complete different question. It's not always important to be right. Sometimes it's smarter not to be.

Last edited:
A graph ##\mathcal{G}## of usually a function ##x \mapsto f(x)## is a set of points: ##\mathcal{G}=\{\,(x,f(x)\,|\,x \in \operatorname{domain}(f)\,\}##. This is a subset of ##\mathbb{R}^2## and to move it means to move it within this plane ##\mathbb{R}^2##. Thus you need a direction in which it is moved and a distance by which it is moved. But this exactly defines a vector ##v=(v_x,v_y)##. So the moved object will be ##v+\mathcal{G}=\{\,(x+v_x,f(x)+v_y\,|\,x \in \operatorname{domain}(f)\,\}##. So in a sense this is even better than just to say move by ##"v_0"## in direction ##"x"## or ##"y"## since you allow more than two directions.

However, whether you should argue with your teacher is a complete different question. It's not always important to be right. Sometimes it's smarter not to be.

So is it okay to write like this ? If i wrote like this In a paper would it be correct ?

fresh_42
Mentor
2021 Award
So is it okay to write like this ? If i wrote like this In a paper would it be correct ?
I'm not quite sure what you mean by this. That's why I wrote the formulas, which are correct. 4 to the left would be ##v_x=-4## and ##v_y=0##. It would be correct, if it would be o.k. depends on a lot of human factors. I wouldn't argue just to be right. 4 to the left is usually as good.

Ray Vickson