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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