SOLUTION: A problem that I have for homework is: "Write an example of a rational function that has asymptotes at x=4 and y=3" How do I find a correct example?

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Question 156721: A problem that I have for homework is:
"Write an example of a rational function that has asymptotes at x=4 and y=3"
How do I find a correct example?
Found 2 solutions by josmiceli, jim_thompson5910:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
A function that has x and y asynptotes is y+=+1%2Fx
When y approaches 0, x approaches infinity
and vice versa.
In order to move the asymptotes to x+=+4 and
y+=+3, I change the equation to y+-+3+=+1+%2F+%28x+-+4%29
or y+=+1+%2F+%28x+-+4%29+%2B+3
plotting this:
+graph%28+700%2C+700%2C+-3%2C+10%2C+-3%2C+10%2C+1+%2F+%28x+-+4%29+%2B+3%29+

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The last solution was perfect, but you can simplify the equation:


y+=+1+%2F+%28x+-+4%29+%2B+3 Start with the given equation


y+=+1+%2F+%28x+-+4%29+%2B+3%28%28x+-+4%29%2F%28x+-+4%29%29 Multiply the second term by %28x+-+4%29%2F%28x+-+4%29


y+=+1+%2F+%28x+-+4%29+%2B+%283%28x+-+4%29%29%2F%28x+-+4%29 Combine the terms.


y+=+1+%2F+%28x+-+4%29+%2B+%283x+-+12%29%2F%28x+-+4%29 Distribute


y+=+%281%2B3x+-+12%29+%2F+%28x+-+4%29 Add the fractions.


y+=+%283x+-+11%29+%2F+%28x+-+4%29 Combine like terms.


So y+=+1+%2F+%28x+-+4%29+%2B+3 simplifies to y+=+%283x+-+11%29+%2F+%28x+-+4%29