SOLUTION: Starting with the graph of {{{ y=3^x }}}, reflect the graph about the line x=-2. Please help me; I missed class on Friday. Thanks.

Algebra ->  Graphs -> SOLUTION: Starting with the graph of {{{ y=3^x }}}, reflect the graph about the line x=-2. Please help me; I missed class on Friday. Thanks.      Log On


   

Question 596183: Starting with the graph of +y=3%5Ex+, reflect the graph about the line x=-2.
Please help me; I missed class on Friday. Thanks.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Step 1) Shift the original graph 2 units to the right. This lines up our desired line of symmetry on the y axis. So we go from y=3%5Ex (green) to y+=+3%5E%28x-2%29 (blue)



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Step 2) Reflect about the y axis (or x = 0) by replacing 'x' with '-x' to get y+=+3%5E%28-x-2%29


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Step 3) Translate back by shifting 2 units to the left. This is done by subtracting off 2 to get the final answer of y+=+3%5E%28-x-4%29


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Answer:

So the graph of y+=+3%5Ex (shown in green) and the reflected graph over the line x = -2, which is y+=+3%5E%28-x-4%29 (shown in blue) are graphed below