Combining transformations
Hello everyone.
My question is that if we have a graph:
f(x) = √(x + 4) - 1
And then we make a new graph that we
- First stretch horizontally about the y - axis by a factor of 1/2
- Then apply a horizontal translation 4 units right
Why is the equation of the graph
g(x) = f(2(x - 4))?
Why is the part of the equation that causes a translation nested inside of the stretch?
Shouldn't the stretch be the thing that applies to x first?
Maybe something like:
g(x) = f(2x - 4) (order of operations means that x is multiplied by 2 first, then subtracted by 4)
But I know I am missing something, because this second form also doesn't make too much sense either. The x - 4 doesn't mean x is being subtracted by four, but rather that x is increasing by four to compensate.
And now I am thoroughly confused. Please help me out.