SOLUTION: Starting with the graph of y = e^x, find the equation of the graph that results from reflecting about the line y=5.

Question 177947: Starting with the graph of y = e^x, find the equation of the graph that results from reflecting about the line y=5.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
In order to reflect about the line y=5, we first need to reflect about the line y=0 (which is much easier). To do that, simply shift the graph 5 units down (to effectively move the line to ). Algebraically, you just subtract 5 from to get

Now to reflect over the line (the x-axis), simply replace "y" with "-y" to get

Multiply both sides by -1 to make y positive.

Now since we shifted down 5 units (ie subtracted 5), we need to shift back up (by adding 5). So add 5 to to get

Add

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Answer:

So after reflecting over the line , we get the equation

Here's a graph to visually verify the answer

Graph of the original equation (red) and the equation (green) which is a reflection over the line (blue)
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