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Can somebody explain f(x+a)

Hello, I know that f(x+a) results in a horizontal translation of -a but I don't understand how this works or how you would plot individual coordinates for this! If somebody could explain it'd be greatly appreciated!
Original post by JakeRStudent
Hello, I know that f(x+a) results in a horizontal translation of -a but I don't understand how this works or how you would plot individual coordinates for this! If somebody could explain it'd be greatly appreciated!


Say you are given a graph f(x)

Just remember that you do the opposite in the bracket. f(x+a) only affects the x co-ordinates. E.g. f(x+2) so all x co-ordinates/values move 2 units to the left/in the negative x-direction

so f(x-5) all x co-ordinates would move 5 units to the right/positive x direction
Original post by KINGYusuf
Say you are given a graph f(x)

Just remember that you do the opposite in the bracket. f(x+a) only affects the x co-ordinates. E.g. f(x+2) so all x co-ordinates/values move 2 units to the left/in the negative x-direction

so f(x-5) all x co-ordinates would move 5 units to the right/positive x direction


I know this but I want to UNDERSTAND why this happens. Can somebody show me step by step how this occurs>=? or go through why it does that to the grraph?
Reply 3
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sabana
20
I never learnt why it happens just got taught the rule :laugh:
Reply 4
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Zacken
22
Original post by JakeRStudent
...


I'd sit down and write out a long explanation about it, but it's 4 a.m where I am, so I'm going to link you to this video ( https://www.youtube.com/watch?v=lwgkUFA7aKQ ) instead, it gives an intuitive feel for why the translations work the way they do. Apologies for not writing something up, I'll see if I can do something in the morning if you're still confused.
Reply 5
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B_9710
18
Well if you have a curve y=f(x) and then say you translate it giving a curve y=f(x+2). When x=0 for the first curve we have y=f(0) right.
To get the same y value for the second curve, we need to make x=-2 to get y=f(0). So this means that the cuvée has been translated 2 units in the negative x direction (to the left).

This is something that I think is very difficult to explain exactly why without the person sitting next to you.
Original post by JakeRStudent
I know this but I want to UNDERSTAND why this happens. Can somebody show me step by step how this occurs>=? or go through why it does that to the grraph?


y = f(x+2) implies that in order to get the original y-coordinate of f(x), we have to set x -> x-2, i.e. x goes to the x value that is 2 to the left of the original one. Since this happens for each point, the whole graph gets translated 2 units to the left.
Original post by JakeRStudent
Hello, I know that f(x+a) results in a horizontal translation of -a but I don't understand how this works or how you would plot individual coordinates for this! If somebody could explain it'd be greatly appreciated!


Say we have curve of function f(x)= x^2. then the curve f(x+a) would be (x+a)^2, meaning the x coordinate of the root of the curve would be at -a as x+a=0. Hence, adding a constant a into the function, it affects the solutions of the curve by -a.
Draw a table of values and you'll see it works.

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