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

[pbonnie]

Homework Statement

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)

Homework Equations

y = ab^k(x-4) + c

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

 

[pbonnie]

Forgot to attach image.

 

[Mark44]

Homework Statement

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)

Homework Equations

y = ab^k(x-4) + c

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

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

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

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

 

[pbonnie]

Oh wow that easy. Great, thanks!