# Graph (x^2+11x+29)/(x+7)

x2+11x+29x+7
Find where the expression x2+11x+29x+7 is undefined.
x=-7
Consider the rational function R(x)=axnbxm where n is the degree of the numerator and m is the degree of the denominator.
1. If n<m, then the x-axis, y=0, is the horizontal asymptote.
2. If n=m, then the horizontal asymptote is the line y=ab.
3. If n>m, then there is no horizontal asymptote (there is an oblique asymptote).
Find n and m.
n=2
m=1
Since n>m, there is no horizontal asymptote.
No Horizontal Asymptotes
Find the oblique asymptote using polynomial division.
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
 x + 7 x2 + 11x + 29
Divide the highest order term in the dividend x2 by the highest order term in divisor x.
 x x + 7 x2 + 11x + 29
Multiply the new quotient term by the divisor.
 x x + 7 x2 + 11x + 29 + x2 + 7x
The expression needs to be subtracted from the dividend, so change all the signs in x2+7x
 x x + 7 x2 + 11x + 29 – x2 – 7x
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 x x + 7 x2 + 11x + 29 – x2 – 7x + 4x
Pull the next terms from the original dividend down into the current dividend.
 x x + 7 x2 + 11x + 29 – x2 – 7x + 4x + 29
Divide the highest order term in the dividend 4x by the highest order term in divisor x.
 x + 4 x + 7 x2 + 11x + 29 – x2 – 7x + 4x + 29
Multiply the new quotient term by the divisor.
 x + 4 x + 7 x2 + 11x + 29 – x2 – 7x + 4x + 29 + 4x + 28
The expression needs to be subtracted from the dividend, so change all the signs in 4x+28
 x + 4 x + 7 x2 + 11x + 29 – x2 – 7x + 4x + 29 – 4x – 28
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 x + 4 x + 7 x2 + 11x + 29 – x2 – 7x + 4x + 29 – 4x – 28 + 1
The final answer is the quotient plus the remainder over the divisor.
x+4+1x+7
The oblique asymptote is the polynomial portion of the long division result.
y=x+4
y=x+4
This is the set of all asymptotes.
Vertical Asymptotes: x=-7
No Horizontal Asymptotes
Oblique Asymptotes: y=x+4
Graph (x^2+11x+29)/(x+7)