myself and a colleague have inherited an exam paper previously used last year for our class and are facing a bit of dispute over naming the function.
The question is written as follows:
the graph is concave upwards
the graph is translated 3 units to the right
the graph is stretched by scale factor 2 in x-axis.
Excuse the poor terminology. They have only looked at quadratics, so concave implies $x^2$.
My colleague has taken the view that the function should be written as
$ f(x) = ( \frac{1}{2} x - 3 )^2 $
However, I argue that it should be $ f(x) = ( \frac{1}{2} (x-3) ) ^2 $.
I am aware given a function $ f(x) $ that has been transformed by $a f(bx + c ) + d $ that the order of transformations should follow $ c, b, a, d $. I can see merit in his answer. But I would argue that since the stretch follows that it means stretching the new substitute of $x-3$ in place of $x$ .
Can anyone shed any light on how they would answer this question? It is poorly written, but I am worried I may just be making a silly error.