document.write( "Question 75944: Please explain how the graph of y=(1/2)^x + 1 can be obtained from the graph
\n" ); document.write( "y=2^x. Thank you. \n" ); document.write( "

Algebra.Com's Answer #54536 by funmath(2933) $\"\"$ $\"About$

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Please explain how the graph of y=(1/2)^x + 1 can be obtained from the graph
\n" ); document.write( "y=2^x. Thank you.
\n" ); document.write( "The graph of y=2^x is found by plotting some points like this:
\n" ); document.write( "x=-2, y=2^(-2)=1/4, (-2,1/4)
\n" ); document.write( "x=-1, y=2^(-1)=1/2, (-1,1/2)
\n" ); document.write( "x=0, y=2^0=1, (0,1)
\n" ); document.write( "x=1, y=2^1=2, (1,2)
\n" ); document.write( "x=2, y=2^2=4, (1,4)
\n" ); document.write( " $\"graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C2%5Ex%29\"$
\n" ); document.write( "y=(1/2)^x+1 can be written as:
\n" ); document.write( "y=2^(-x)+1
\n" ); document.write( "So your graph of y=2^x will be reflected about the y-axis because of the -x
\n" ); document.write( "It will also be shifted up vertically because of the +1.
\n" ); document.write( "Ultimately, it looks like this:
\n" ); document.write( " $\"graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C%281%2F2%29%5Ex%2B1%29\"$
\n" ); document.write( "If you multiply all the x's you plotted for the first graph by -1 and then added 1 to all their corresponding y's you'll have points to plot for this graph.
\n" ); document.write( "Happy Calculating!!! \n" ); document.write( "

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