1. ## shifting curves

The graph, y=f(x) has been transformed to y= af[ b(x-h) ] + k. Determine the values of a, b, h and k.

(1) Vertical expansion by a factor of 2, then a translation of 5 units left and 2 units up.
Answer key: a=2, b=1, h= -5 k=2

My workings:
y = 2f(x+5) + 2

Therefore, a=2, b=1, h= 5 k=2

Why is the answer key h= -5? Translation of 5 units left makes x=-5, so (x+5) and I can see that h is replaced by +5.

(2) A translation of 6 units right, then horizontal compression by a factor of 1/2 and a reflection in the x-axis.
Answer key: a=-1, b=2, h= 3 k=0

My workings:
y = -f[2(x-6)]

Therefore, a=-1, b=2, h= -6 k=0

Why is the answer key h= 3? Maybe I need to foil the expression such that:
2(x-6) = 0
2x -12 = 0
2x = 12
x=6
Even if I foil the expression, I should get 6 and not 3.

2. Originally Posted by shenton
The graph, y=f(x) has been transformed to y= af[ b(x-h) ] + k. Determine the values of a, b, h and k.

(1) Vertical expansion by a factor of 2, then a translation of 5 units left and 2 units up.
Answer key: a=2, b=1, h= -5 k=2

My workings:
y = 2f(x+5) + 2

Therefore, a=2, b=1, h= 5 k=2

Why is the answer key h= -5? Translation of 5 units left makes x=-5, so (x+5) and I can see that h is replaced by +5.
But the formula uses f(x - h) and you have f(x + 5). Thus x - h = x + 5 ==> h = -5.

Originally Posted by shenton
(2) A translation of 6 units right,
y = f(x - 6)

Originally Posted by shenton
then horizontal compression by a factor of 1/2
y = f(2x - 6)
(You transformed the whole of x - 6, not just the x.)

Originally Posted by shenton
and a reflection in the x-axis.
y = -f(2x - 6) = -f(2[x - 3])