Homework Help: Transformations of y = ab^k(x-4) + c

1. Feb 21, 2013

pbonnie

1. The problem statement, all variables and given/known data
Describe the transformations that must be applied to the graph of y = 5^x to obtain the graph of y = 2 - 3(5^(x+4)) and complete the following table (attached)

2. Relevant equations
y = ab^k(x-4) + c

3. The attempt at a solution
I started filling out the table. First column was provided.
Second column y = -3(5^x) I multiplied the y value by -3
(-1,-3/6)
(0,0)
(1,-3)
(2,-6)
(3,-9)

For the third column I'm not sure how to incorporate the 2-3. I know the graph shifts 4 units left, so I would subtract 4 from each x value. But that's all I understand.
(-5, ?)
(-4, ?)
(-3, ?)
(-2, ?)
(-1, ?)

I can answer the rest of the question once I figure out how to do this part.
Thank you

2. Feb 21, 2013

pbonnie

Forgot to attach image.

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3. Feb 21, 2013

Staff: Mentor

Don't think of it as "2 - 3", since they represent different transformations.

First look at y = 5x + 4, which represents a shift to the left by 4 units relative to the graph of y = 5x.

Next, look at y = 3*5x + 4.
Then look at y = -3*5x + 4.
Finally, look at y = -3*5x + 4 + 2, which is the same as y = 2 - 3*5x + 4.

4. Feb 22, 2013

pbonnie

Oh wow that easy. Great, thanks!