The Student Room Group

on a graph with f(x)= (x-3), why would you move it right?

the question is in the title, I mean, SURLY IT MAKES SENSE TO GO 3 LEFT AS ITS A MINUS?????? (and not 3 to the right)
Reply 1
Original post by Azimbrook1
the question is in the title, I mean, SURLY IT MAKES SENSE TO GO 3 LEFT AS ITS A MINUS?????? (and not 3 to the right)


edit:here I'm talking about translation of graphs
Original post by Azimbrook1
edit:here I'm talking about translation of graphs

Haven't touched maths in a while but i'd say just think of the graph itself and how it would look. If you had the graph y=x, y=0 when x=0. In other words, the graph goes through (0,0). If you have y=x-3, y=0 when x=3. So it goes through (3,0) i.e. 3 units to the right of (0,0). That's the way I remembered it, not sure if it works for everybody.
Reply 3
Draw the graph of y=x. On the same axes draw the line y=(x-3). See how the graph has moved. I find a picture helps me to see something more easily.
y = f(x-3)

This means The Y-coordinate for any value of X will be equal to the Y-coordinate of the 3 Xs to the left.

So for any X-coordinate you take its Y-coordinate as the one from 3 units to the left.

So you translate to the right by teleporting from the left.

Hope that makes sense.
Original post by CuriosityYay
teleport

nice
Original post by JJJJJAAAAMES
nice

:hat2:
Reply 7
f(x-3) means that all the inputs are reduced by 3. The way I tried to understand it is, "because all the inputs are lowered by 3, everything in the graph happens later, so it moves to the right". And vice versa for f(x+3).
Original post by Azimbrook1
the question is in the title, I mean, SURLY IT MAKES SENSE TO GO 3 LEFT AS ITS A MINUS?????? (and not 3 to the right)


Firstly this is a bad example for someone beginning this topic and I'll explain why. Firstly, I'm going to change what's in your title to;

f(x)=x    f(x3)=x3 f(x) = x \implies f(x-3) = x-3

The reason this is a bad example for a beginner is because f(x)=x    f(x)3=x3 f(x) = x \implies f(x) - 3 = x-3
and then you will get confused as to why the second one seems intuitive , why the first one doesn't and why are they both the same.

Now think of any curve on a graph. There is a machine f where you can put any number which we call xx into the machine f and f spits out the number f(x)f(x) which is the value on the yy coordinate (the output).

So this means if we have know f(x) f(x) and we put x=2x=2 into the machine then it spits out the number f(2) f(2) then there's an altercation to the machine where it now spits out the number f(x-a) rather than f(x), now what value of x do we need to put in the altered version of the machine to obtain the value f(2)? Let's try x=2+ax=2+a (draw this on the x axis - can you see that 2+a is to the right of 2 Now f(2+a-a) = f(2).

So what this says is that for every number we plug into the original machine x to obtain the value f(x), we would need to plug in x+a, which is further to the right of the x axis than x by a units to obtain f(x).

Let's try a numerical example f(x)=2xNowf(4)=2(4)=8f(x) = 2x \mathrm{Now} \, f(4) = 2(4) = 8

Now let's work out how to obtain 8fromthefunctionf(x3).f(x3)=8    2(x3)=8    x=78 \quad \mathrm{from \quad the \quad function} f(x-3). \quad f(x-3) = 8 \implies 2(x-3) = 8 \implies x=7

Can you see that this means originally what we plug in moves to the right by 3 3 units and we know need to plug in an x value 3 units to the right to obtain identical outputs as the original.

So all you need to ask yourself is what values do we need to put in the shifted function to obtain output values which are the same as the outputs of the original function. Are they values to the left or to the right on the x axis?
I like to think of it this way.

The graph y must always equal a function of x.
Therefore y = f(x).

Say we have a function f(x-7).
If we add 7 to the x part of the function we have f(x).
this is the same as moving the co-ordinates 7 to the right

f(x-7+7) = f(x).

Now lets say instead we have the equation y = f(x-7) + 5.

As we discussed before y must equal f(x) so, add 7 to the x-coordinates

when we do so, we have: y = f(x) + 5 as our function of x. Instead of our original y = f(x-7) + 5.

Congrats you found the y = f(x) value.

The reason we add 5 instead of subtract 5 is because we dont need to find the f(x) value anymore. So essentially were saying whatever our function of x, add 5 to it and equate it to y.

Thats why you move the y-coordinate up by 5

Might be a little confusing but i'd recommend you keep reading this till it clicks
(edited 1 year ago)
Original post by Azimbrook1
the question is in the title, I mean, SURLY IT MAKES SENSE TO GO 3 LEFT AS ITS A MINUS?????? (and not 3 to the right)


I mean just think about what your doing to the function f(x) = x -3, to convert it from g(x) = x.

it actually makes perfect sense, thats the thing with maths, the right answer is the logical/rational path...

Quick Reply

Latest