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

Algebra ->  Functions -> SOLUTION: Starting with the graph of y = e^x, find the equation of the graph that results from reflecting about the line y=5.      Log On


   

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) About Me  (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 y=e%5Ex 5 units down (to effectively move the line y=5 to y=0). Algebraically, you just subtract 5 from e%5Ex to get


y=e%5Ex-5


Now to reflect over the line y=0 (the x-axis), simply replace "y" with "-y" to get


-y=e%5Ex-5


y=-e%5Ex%2B5 Multiply both sides by -1 to make y positive.


Now since we shifted y=e%5Ex down 5 units (ie subtracted 5), we need to shift y=-e%5Ex%2B5 back up (by adding 5). So add 5 to y=-e%5Ex%2B5 to get

y=-e%5Ex%2B5%2B5


y=-e%5Ex%2B10 Add


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Answer:

So after reflecting y=e%5Ex over the line y=5, we get the equation y=-e%5Ex%2B10


Here's a graph to visually verify the answer

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+exp%28x%29%2C+-exp%28x%29%2B10%2C5%29+ Graph of the original equation y=e%5Ex (red) and the equation y=-e%5Ex%2B10 (green) which is a reflection over the line y=5 (blue)