In the equation #y = afb(x + c) +d#, #a# represents a vertical stretch or compression. Since #|a| > 1#, this will involve a vertical stretch by a factor of #2#. Since #a# is smaller than #0#, the graph will have a reflection over the x-axis.
Next, let's factor the parentheses so that the #x# term has a coefficient of #1#.
#-2x + 1 = -2(x - 1/2)#
So, we can rewrite our function transformation as #y = -2f(-2(x - 1/2)) + 3#. Here, #b = -2#.
#b# means a horizontal compression by a factor of #1/2#, because #|b| > 1#. There will also be a reflection over the y-axis, considering that #b < 0#.
#c# is the horizontal displacement. Since #c < 0#, the graph will shift #1/2# a unit to the right.
#d# is the vertical displacement. Since #d > 0#, the graph will move #3# units up.
Hopefully this helps!
