anonymous
  • anonymous
identify the vertical and horizontal asymptote for f(x)=(x^2+3)/(x-4).
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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experimentX
  • experimentX
as x tends to 4, the value of f(x) tends to infinity from both sides, you can say x=4 is one horizontal asymptote
anonymous
  • anonymous
A plot is attached.
1 Attachment
anonymous
  • anonymous
finding the vertical asymptotes are easy... just set each factor in the denominator = 0 and solve. the x-values that makes the denominator 0 will (MOST of the time) be your vertical aymptote.

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anonymous
  • anonymous
for horizontal asymptotes to occur, the degree on the numerator has to be equal (or less) than the degree of the denominator. if the degree of the numerator is less than the degree of the denominator, then the line y=0 is your horizontal asymptote.
anonymous
  • anonymous
if the degree of the numerator is equal to the degree of the denominator, then y=a/b is your asymptote, where a, b are the coefficients of the terms with the highest degree.
anonymous
  • anonymous
for this function, f(x)=(x^2+3)/(x-4), the degree on the top is greater than the degree on the bottom. There is no horizontal asymptote here.
anonymous
  • anonymous
but there is a slant asymptote...

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