SOLUTION: Take the basic graph of f(x) = 2^x. Now we are going to perform a transformation: f(x) = 2^(-x +3). The graph of this function is the graph of the original function reflected acros

Algebra ->  Finance -> SOLUTION: Take the basic graph of f(x) = 2^x. Now we are going to perform a transformation: f(x) = 2^(-x +3). The graph of this function is the graph of the original function reflected acros      Log On


   

Question 1118317: Take the basic graph of f(x) = 2^x. Now we are going to perform a transformation: f(x) = 2^(-x +3). The graph of this function is the graph of the original function reflected across the y axis. We also have a horizontal shift, and it is here that I have a question. My understanding is that a +3 would cause a shift to the left of 3. However, when I plot this function using a graphing utility it is shifted to the right. Why do I see this discrepancy?
Thanks.
David
dmurley@acm.org
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
the graph of y = 2^x(red line) and y = 2^(-x+3)(green line) looks like this
:
+graph%28+300%2C+200%2C+-2%2C+7%2C+-1%2C+7%2C+2%5Ex%2C+2%5E%28-x%2B3%29%29+
:
if the second function were y = 2^(x+3), we get the horizontal shift to the left
:
+graph%28+300%2C+200%2C+-7%2C+7%2C+-1%2C+7%2C+2%5Ex%2C+2%5E%28x%2B3%29%29+
:
we have a -x in the original equation, the -1 is a horizontal scale which divides each x value by -1, which causes a reflection about the y axis