document.write( "Question 74437: Starting with the graph of f(x)= 7^x Write the equation of the graph that results from reflecting f(x) about the line y= -1 y= ? \n" ); document.write( "

Algebra.Com's Answer #53444 by jim_thompson5910(35256) $\"\"$ $\"About$

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If you reflect the equation $\"y=7%5Ex\"$ across the y=0 line you get this graph $\"y=-7%5Ex\"$ since each y value is now the opposite. If we're doing this across the y=-1 line, we get the same thing, but it's shifted. Since the graph $\"y=7%5Ex\"$ hits the y-axis at (0,1) it is 2 units away from the line y=-1. So the intercept of the reflected graph is 2 units away from the line y=-1 (which is (0,-3). So the equation is $\"y=-7%5Ex-2\"$ since the general equation of a exponential function is $\"y=ab%5Ex%2Bc\"$ where c+1 is the intercept (ie the intercept is (0,c+1). Since the entire thing is negated it looks like
\n" ); document.write( " $\"y=-%28ab%5Ex%2Bc%29\"$ where c-1 is the intercept.\r
\n" ); document.write( "\n" ); document.write( " $\"graph%28+300%2C+200%2C+-3%2C+2%2C+-5%2C+5%2C+7%5Ex%2C+-1%2C+-7%5Ex-2%29+\"$ Equations $\"y=7%5Ex\"$ (red) , $\"y=-7%5Ex-2\"$ (dark blue), and the line of reflection y=-1 (green). \n" ); document.write( "

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