Question on transformation of functions

[thepositiveclub]

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

[Vioh]

When translating a function f(x) = 2(x −1)²by a vector (3, -2), will it transform into 2(x −4)² - 2 or 2(x +2)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

[thepositiveclub]

 

When translating a function f(x) = 2(x −1)²by a vector (3, -2), will it transform into 2(x −4)² - 2 or 2(x +2)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!