If given the function f(x) = x^2 and asked to write the result of translating the function 1 unit to the left. Is the following correct? Explain. g(x) = (x+1)^2    Is writing g(x) the same as...

If given the function f(x) = x^2 and asked to write the result of translating the function 1 unit to the left. Is the following correct? Explain.

g(x) = (x+1)^2

 

 

Is writing g(x) the same as writing f(x)?

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Yes your answer is correct.   No g(x) != f(x).  g(x) is f(x) translated left by one unit.  

The general translation of a function f(x) by h unitis horizontially (in this case h=-1) and k units vertacally is `g(x)=f(x-h)+k` .

So in our case we are translatting a function -1 units horizontally (one unit to the left), and 0 units vertically, we get

`g(x) = f(x-(-1)) + 0 = f(x+1)`

Since `f(x) = x^2` we get

`g(x) = (x+1)^2`

I hope that helps...

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