I have got a very simple problem. I have an exercise:
If $\ f(x) = 2x^2 − 4$, give the function which shows the graph of $\ f(x)$ after vertical stretch of scale factor $\ 0.5 $ followed by a translation $\binom{-4}{0}$
The answer that I get is $\ f(x)=x^2+8x+14 $, but the answer given is $\ f(x)=8x^2+64x+124 $. In my opinion, the answer that is given can certainly be achieved, but using horizontal translation instead of vertical. After drawing a graph of my function and the given function I noticed that in my case the function is compressed (its "branches" are closer to the x – axis than the original one) – as it should be, as scale factor is less than 1.
Am I wrong there, or is something wrong with answers? I would not have asked the question, but I noticed that there is at least one more question about which I am uncertain as much as about this one, thus, I need to find out the real answer.
Best Answer
You are right.
We are looking for the function \begin{align}\frac12f(x+4)&=\frac12(2(x+4)^2-4)\\&=(x+4)^2-2\\ &=x^2+8x+14 \end{align}
Of course, there is a possibility that you course is asking the wrong question as well.