How do you find holes in graphs? Stuck?
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I needed to find Vertical Asymptotes, Horizontal Asymptotes, Domains, and holes in the graphs below, but I can't figure out/ remember how to find holes in graphs. I don't think these have them but I'm not sure. I don't know how to find holes algebraically, only using a calculator. #6 f(x)= ( x (x+2) )/(-x^2+2x) Horizontal Asymptote=-1 Vertical Asymptote=2 Hole(s)=? Domain= x=/=0 , x=/=2 #7 f(x)= (4(x+1)/x(x-4) Horizontal Asymptote= y=0 Vertical Asymptote= x=0 x=4 Holes=? Zero(s)= x=-1 #9 Find any holes in the graph of f(x)= x^2 -2x -8 / x^2 - 16 Any help would be appreciated. Thank You!
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Answer:
The numerator and denominator need to cancel so in (x+1)/((x+1)(x-1)) the hole would be at -1
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Other answers
when u find two of the same for ur example it would be x-4 and x+2 / x-4 and x+4 so the double is x-4 and x=4 is where the whole is...
when u find two of the same for ur example it would be x-4 and x+2 / x-4 and x+4 so the double is x-4 and x=4 is where the whole is...
I AM BLACK WHERE IT COUNTS
The numerator and denominator need to cancel so in (x+1)/((x+1)(x-1)) the hole would be at -1
Tyler
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