SOLUTION: please help me with this....Find the vertical, horizontal, and oblique asymptotes, if any, for the given rational function.
Q(x)=(3x^2-11x-4)/(2x^2-7x-4)
Algebra.Com
Question 1157588: please help me with this....Find the vertical, horizontal, and oblique asymptotes, if any, for the given rational function.
Q(x)=(3x^2-11x-4)/(2x^2-7x-4)
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20855) (Show Source): You can put this solution on YOUR website!
Horizontal asymptote:
find quotient of highest degree of variable
-> as -> ±
Vertical asymptote:
find values excluded from domain
->
-> ± as ->
-> as ->
=> Vertical asymptote:
oblique asymptote:
since numerator and denominator have same highest degree of variable , there is asymptotes
Answer by greenestamps(13334) (Show Source): You can put this solution on YOUR website!
(1) Horizontal or oblique asymptotes
The degrees of the numerator and denominator are the same, so there is a horizontal asymptote and no oblique asymptote.
The ratio of the leading coefficients gives you the horizontal asymptote.
ANSWER: Horizontal asymptote at y = 3/2.
(2) Vertical asymptotes
Vertical asymptotes will occur wherever there is a linear factor in the denominator that is not also in the numerator.
Factor numerator and denominator:
There is a vertical asymptote were the factor (2x+1) in the denominator is equal to 0.
ANSWER: There is a single vertical asymptote, at x = -1/2.
What about the factors (x-4) in both numerator and denominator?
For x=4, the denominator is 0 and so the function is undefined. For all other values of x, the function is equivalent to . So the graph of the given function is the same as the graph of except that there is a hole in the graph at x=4.
RELATED QUESTIONS
find the vertical, horizontal, and oblique asymptotes, if any, for the following rational (answered by stanbon)
Find the vertical, horizontal, and oblique asymptotes, if any for the given rational... (answered by lwsshak3)
please help me with this problem....Find the vertical, horizontal, and oblique... (answered by jim_thompson5910)
Show work, find the vertical, horizontal, and oblique asymptotes of any for the given... (answered by lynnlo)
12- Show work, find the vertical, horizontal, and oblique asymptotes of any for the given (answered by stanbon)
For the following function find the vertical, horizontal, and oblique asymptotes, if any. (answered by lwsshak3)
8. For the following function find the vertical, horizontal, and oblique asymptotes, if... (answered by stanbon)
8. For the following function find the vertical, horizontal, and oblique asymptotes, if... (answered by lwsshak3)
Find all the asymptotes, x-intercepts, and y-intercepts for the graph of the given... (answered by CubeyThePenguin,ikleyn)