anonymous
  • anonymous
Describe the vertical asymptote(s) and hole(s) for the graph of y = (x+2)(x+4)/(x+4)(x+1)
Mathematics
jamiebookeater
  • jamiebookeater
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jim_thompson5910
  • jim_thompson5910
does anything cancel in (x+2)(x+4)/(x+4)(x+1)
anonymous
  • anonymous
1?
jim_thompson5910
  • jim_thompson5910
notice you have a pair of "x+4" terms

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jim_thompson5910
  • jim_thompson5910
so they would cancel
anonymous
  • anonymous
Ok so the hole is 4?
jim_thompson5910
  • jim_thompson5910
close, the hole is actually -4, this is because (x+2)(x+4)/(x+4)(x+1) simplifies to (x+2)/(x+1) it has a vertical asymptote at x = -1 because this makes the denominator x+1 equal to zero but to make (x+2)(x+4)/(x+4)(x+1) equivalent to (x+2)/(x+1), you have to add the further restriction that x can't equal -4, which causes the hole there
anonymous
  • anonymous
so the asymptote is -1? this is much clearer lol thank you!!1
jim_thompson5910
  • jim_thompson5910
yes it is, yw

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