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!
