SOLUTION: Take the graph of y=2^x and transform it into y= -3(2)^(2x-4). Label 3 key points on both graphs. I've tried graphing it and applying the required stretches and transformations

Algebra ->  Equations -> SOLUTION: Take the graph of y=2^x and transform it into y= -3(2)^(2x-4). Label 3 key points on both graphs. I've tried graphing it and applying the required stretches and transformations       Log On


   

Question 724219: Take the graph of y=2^x and transform it into y= -3(2)^(2x-4). Label 3 key points on both graphs.
I've tried graphing it and applying the required stretches and transformations (vertical stretch by 3, horizontal stretch by 1/2, reflection on x-axis, horizontal translation 4 units left) but my graph doesn't match the graph I plug into the calculator. Am I doing something wrong?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Assuming you meant y equals x squared (y=x^2):
To transform y=x%5E2 into y=-3%282x-4%29%5E2
you need a horizontal translation by 2 units right,
because you replaced z=x-2 by x and then by 2z=2%28x-2%29=2x-4.
A little algebra to get a simplified formula for the same function could have helped:
y=-3%282x-4%29%5E2 --> y=-3%282%28x-2%29%29%5E2 --> y=-3%282%5E2%28x-2%29%5E2%29 --> y=-3%284%28x-2%29%5E2%29 --> y=-12%28x-2%29%5E2
Then you would need a vertical stretch by 12, reflection on x-axis, and horizontal translation 2 units right.

NOTE: If you meant y=sqrt%28x%29 and y=-3sqrt%282x-4%29
the same thing applies.
z%28x%29=%28x-2%29 puts z 2 units to the left by subtracting 4, but
in the compound function f%28g%28x%29%29, to get the same y value you need to add 4 to x:
f%28z%2B2%29=f%28x-2%2B2%29=f%28%28x%2B2%29-2%29=f%28x%29=y