asymptotes

[trist666]

I think I got the correct answer to this question, but maybe someone smart can tell me if I'm really right or not. The question is:
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Determine the equations of any asymptotes for the function y= x+7
For the asymptote equations I got y= 3/7 and x=(-4)

Are the answers right?

 

[Unco]

y=3/7 is the y-intercept, found by setting x=0, but that has nothing to do with asymptotes. Nor does x=-4 which is what x is when y=1.


Vertical asymptote: set the denominator to zero --> x = ?

Horizontal asymptote: consider where y goes as x gets very large in either direction. If you divide top and bottom by x you get y = (3/x)/(1 + 7/x), and as x gets large, 3/x and 7/x tend to zero so we are left with y=0/1.