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algebra2sucks

  • 3 years ago

Describe the vertical asymptote(s) and hole(s) for the graph of y = (x+2)(x+4)/(x+4)(x+1)

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  1. jim_thompson5910
    • 3 years ago
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    does anything cancel in (x+2)(x+4)/(x+4)(x+1)

  2. algebra2sucks
    • 3 years ago
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    1?

  3. jim_thompson5910
    • 3 years ago
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    notice you have a pair of "x+4" terms

  4. jim_thompson5910
    • 3 years ago
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    so they would cancel

  5. algebra2sucks
    • 3 years ago
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    Ok so the hole is 4?

  6. jim_thompson5910
    • 3 years ago
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    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

  7. algebra2sucks
    • 3 years ago
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    so the asymptote is -1? this is much clearer lol thank you!!1

  8. jim_thompson5910
    • 3 years ago
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    yes it is, yw

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