Pessimist Singularitarian

#6
September 17th, 2016,
01:49
Suppose we are given a function $f(x)$ and we wish to shift the graph of that function horizontally. If we wish to shift the function to the left $k$ units, then we can think of accomplishing this by moving our coordinate axes horizontally to the right $k$ units, that is:

$ \displaystyle X=x+k$

So now what we have is that:

$ \displaystyle f(X)=f(x+k)$

is the graph of $f(x)$ shifted to the left by $k$ units. Now, in this problem, we are given the function:

$ \displaystyle y(x)=(x-1)^2-6$

And we are told to shift it 1 unit to the left.

So, in terms of what I posted above, we have $y=f,\,k=1$ and so there results:

$ \displaystyle y(x+1)=((x+1)-1)^2-6=x^2-6$