document.write( "Question 1167485: Given p(x) = x^3+5x^2+4x/3(x+1)(x^2−7x+12),
\n" ); document.write( "find:
\n" ); document.write( "(a) X-intercept(s)
\n" ); document.write( "(b) Y-intercept
\n" ); document.write( "(c) Vertical asymptote(s)
\n" ); document.write( "(d) Hole(s)
\n" ); document.write( "(e) End behavior / horizontal asymptote \n" ); document.write( "

Algebra.Com's Answer #792073 by solver91311(24713) $\"\"$ $\"About$

You can put this solution on YOUR website!
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-intercepts are the points

where each

is a real zero of the numerator function. The

-intercept is the point

where

and

is the numerator function. There is a vertical asymptote at the line

for each factor

of the denominator function that is not also a factor of the numerator function. There is a hole where ever a linear factor of the denominator has a common linear factor in the numerator.\r
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\n" ); document.write( "\n" ); document.write( "Horizontal asymptotes:\r
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\n" ); document.write( "\n" ); document.write( "Case 1: The degree of the numerator polynomial is smaller than the degree of the denominator polynomial -- the line

(i.e. the

-axis) is the horizontal asymptote.\r
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\n" ); document.write( "\n" ); document.write( "Case 2: The degree of the numerator polynomial is equal to the degree of the denominator polynomial -- the line

where

is the lead coefficient of the numerator polynomial and

is the lead coefficient of the denominator polynomial.\r
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\n" ); document.write( "\n" ); document.write( "Case 3: The degree of numerator polynomial is greater than the degree of the denominator polynomial -- there is no horizontal asymptote, rather there is a slant asymptote. The RHS of the equation of the slant asymptote is the quotient obtained from performing polynomial long division excluding any remainder.\r
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\n" ); document.write( "John
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\n" ); document.write( "My calculator said it, I believe it, that settles it
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\r
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\n" ); document.write( "\n" ); document.write( "I > Ø
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