# Question on transformation of functions

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When translating a function f(x) = 2(x âˆ’1)2by a vector (3, -2), will it transform into 2(x âˆ’4)- 2 or 2(x +2)- 2 and why? Thanks in advance!

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When translating a function f(x) = 2(x âˆ’1)2by a vector (3, -2), will it transform into 2(x âˆ’4)- 2 or 2(x +2)- 2 and why? Thanks in advance!

According to the theory, transforming a graph f(x) by 'n' units to the right would give you the graph of f(x-n). On the other hand, if you want to translate 'n' units to the left, you would get the graph of f(x+n). So for your question, since you want to translate 3 units to the right, you just need to replace 'x' in your original function with 'x-3' --> f(x-3) = 2((x-3)-1)^2 = 2(x-4)^2. The answer is thus 2(x-4)^2 - 2

The reason why the theory says so might be a little hard to explain. But if you really want to know, I can give it a try

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When translating a function f(x) = 2(x âˆ’1)2by a vector (3, -2), will it transform into 2(x âˆ’4)- 2 or 2(x +2)- 2 and why? Thanks in advance!

According to the theory, transforming a graph f(x) by 'n' units to the right would give you the graph of f(x-n). On the other hand, if you want to translate 'n' units to the left, you would get the graph of f(x+n). So for your question, since you want to translate 3 units to the right, you just need to replace 'x' in your original function with 'x-3' --> f(x-3) = 2((x-3)-1)^2 = 2(x-4)^2. The answer is thus 2(x-4)^2 - 2

The reason why the theory says so might be a little hard to explain. But if you really want to know, I can give it a try

That's perfect, thank you so much!

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