document.write( "Question 858672: orginal graph is y=4^x. I need to rewrite the equation and redraw graph showing a reflection about the y axis and a dilation of 1/2. I think for the reflection it is y=4^-x but don't know what to do about the dilation. \n" ); document.write( "

Algebra.Com's Answer #517324 by rothauserc(4718) $\"\"$ $\"About$

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We are given y=4^x and asked to show a reflection about the y axis and a dilation of 1/2.
\n" ); document.write( "first rewrite the equation using function notation
\n" ); document.write( "f(x) = 4^x
\n" ); document.write( "now
\n" ); document.write( "f(-x) = 4^-x = 1/4^x
\n" ); document.write( "dilation is a scale factor on the function, since we are showing a reflection about the y axis, we will use vertical dilation, therefore
\n" ); document.write( "f(x) = (1/2)*1/4^x
\n" ); document.write( "here is the graph of both equations (red line is f(x) = 4^x, green is reflection with vertical dilation)
\n" ); document.write( " $\"+graph%28+300%2C+200%2C+-10%2C+10%2C+-10%2C+10%2C+4%5Ex%2C+1%2F2+%2A+1%2F4%5Ex%29+\"$
\n" ); document.write( " \n" ); document.write( "

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