document.write( "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?\r
\n" ); document.write( "\n" ); document.write( "Thanks.\r
\n" ); document.write( "\n" ); document.write( "David
\n" ); document.write( "dmurley@acm.org \n" ); document.write( "

Algebra.Com's Answer #733587 by rothauserc(4718) $\"\"$ $\"About$

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
\n" ); document.write( ":
\n" ); document.write( " $\"+graph%28+300%2C+200%2C+-2%2C+7%2C+-1%2C+7%2C+2%5Ex%2C+2%5E%28-x%2B3%29%29+\"$
\n" ); document.write( ":
\n" ); document.write( "if the second function were y = 2^(x+3), we get the horizontal shift to the left
\n" ); document.write( ":
\n" ); document.write( " $\"+graph%28+300%2C+200%2C+-7%2C+7%2C+-1%2C+7%2C+2%5Ex%2C+2%5E%28x%2B3%29%29+\"$
\n" ); document.write( ":
\n" ); document.write( "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 \n" ); document.write( "

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