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Help with vector notation

  • Thread starter R_Sarav
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  • #1
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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.
 

Answers and Replies

  • #2
12,689
9,235

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.
 
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  • #3
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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 ?
 
  • #4
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9,235
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.
 
  • #5
Ray Vickson
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Homework Helper
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So is it okay to write like this ? If i wrote like this In a paper would it be correct ?
It is correct, but I suspect that if you wrote it like fresh_42 did your teacher would really yell at you.

If I were your teacher, what I would prefer to see are either of the following (assuming you are graphing a parabola of the form ##y = a + b x^2##). If you want to move the whole graph ##A## units to the right (to the left if ##A < 0##) and ##B## units up (down if ##B < 0##), you could either say that (i) the vertex moves from ##(a,0)## to ##(a+A, 0+B)## but the shape remains unchanged; or (ii) explain that the new graph has equation ##y-B = a + b(x-A)^2 \Rightarrow y = a+B+b(x-A)^2.## Since you are plotting graphs in two-dimensional cartesian coordinate systems, I don't think you could be yelled at for doing it using method (i). However, my personal preference would be that you show your understanding by using method (ii).
 

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