Question 192035: In the equation 5x/(x+1), what is the end behavior? We are being taught the Ratey method and when I get to the E part of Ratey, i simplify it to 5/1. Does that make it top heavy? If so how do you determine the vertical asymptote?
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! 5x /(x+1)
vertical asymptote at den =0, x+1=0, x=-1
as degrees num and den equal, hor asymptote at 5/1 = +5
sketch vertical line at x=-1, and horizontal line at y=+5
rough sketch shows function starting low at x=-1, rising to rt thru (0,0) to just under asy y=5
starting high at x=-1, function decays to just above hor asy at y=5 as it goes to left
end behavior: as x approaches -infinity, y approaches +5 from +side
as x approaches + infinity, y approaches +5 from - side
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