SOLUTION: What equation would have the translation of y=4/x and has the asymtopes x=-7 ; y=2?

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Question 970346: What equation would have the translation of y=4/x and has the asymtopes x=-7 ; y=2?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Original: y+=+4%2Fx

Shift it 7 units left. Replace x with x+7: y+=+4%2F%28x%2B7%29
Notice how x = -7 makes the denominator zero, leading to a vertical asymptote

Finally, shift it up 2 units: y+=+4%2F%28x%2B7%29%2B2

So y+=+4%2F%28x%2B7%29%2B2 has the asymtopes x=-7 (vertical asymptote) ; y=2 (horizontal asymptote)

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Side note:

y+=+4%2F%28x%2B7%29%2B2 can be rewritten as...


y+=+4%2F%28x%2B7%29%2B2

y+=+4%2F%28x%2B7%29%2B2%2A%28x%2B7%29%2F%28x%2B7%29

y+=+%284%2B2%2A%28x%2B7%29%29%2F%28x%2B7%29

y+=+%284%2B2x%2B14%29%2F%28x%2B7%29

y+=+%282x%2B18%29%2F%28x%2B7%29

y+=+%282%28x%2B9%29%29%2F%28x%2B7%29


So y+=+4%2F%28x%2B7%29%2B2 is the same as y+=+%282x%2B18%29%2F%28x%2B7%29 and y+=+%282%28x%2B9%29%29%2F%28x%2B7%29