I am currently preparing for my Maths level-2 subject SAT'S and I came across a question that I am finding difficulty in.
Q) Which of the following is the transformation of y=f(x) that translates this function down 3, shrinks it horizontally by a factor of 2, and reflects it about the x-axis?
My Logic:-
y=f(x)
After translating it 3 units down
y=f(x)-3
After shrinking it horizontally by a factor of 2
y=f(2x)-3
Since reflection of any function y=g(x) about the x-axis is y=-g(x)
The reflection of f(2x)-3 about the x-axis should be -[f(2x)-3]= -f(2x)+3
However, Barron's states that the right answer is y=-f(2x)-3 since it first decides to shrink it followed by reflecting it and then translating it. My question is that shouldn't the order of the question be followed while transforming?? Awaiting a response. Regards