Question

Give the equations of any​ vertical, horizontal, or oblique asymptotes for the graph of the rational function.
f left parenthesis x right parenthesis equals StartFraction 4 minus 6 x Over 3 x plus 4 EndFraction
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Part 1
Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The equation of the vertical asymptote is xequals
  
enter your response here.
​(Type an integer or a fraction. Simplify your​ answer.)
B.
There is no vertical asymptote.
Part 2
Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The equation of the horizontal asymptote is yequals
  
enter your response here.
​(Type an integer or a fraction. Simplify your​ answer.)
B.
There is no horizontal asymptote.
Part 3
Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The equation of the oblique asymptote is yequals
  
enter your response here.
​(Type an integer or a fraction. Simplify your​ answer.)
B.
There is no oblique asymptote.

Answer 1

Part 1 (vertical): A. x = -4/3 (since 3x+4 = 0 → x = -4/3 and numerator ≠ 0 there)

Part 2 (horizontal): A. y = -2 (degrees equal, horizontal asymptote = ratio of leading coefficients −6/3 = −2)

Part 3 (oblique): B. There is no oblique asymptote (degrees are equal, so no slant asymptote).