Question

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Part 1
Give the equations of any​ vertical, horizontal, or oblique asymptotes for the graph of the rational function.
​f(x)equalsStartFraction x squared minus 6 Over x plus 3 EndFraction
Question content area bottom
Part 1
Select the correct answer 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 simplified​ fraction.)
B.
There is no vertical asymptote.
Part 2
Select the correct answer 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 simplified​ fraction.)
B.
There is no horizontal asymptote.
Part 3
Select the correct answer 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 simplified​ fraction.)
B.
There is no oblique asymptote.

Answer 1

Part 1 — Vertical asymptote:
A. x = -3
(denominator zero at x = -3 and numerator ≠ 0 there)

Part 2 — Horizontal asymptote:
B. There is no horizontal asymptote
(degree numerator > degree denominator)

Part 3 — Oblique asymptote:
A. y = x - 3
(since (x^2 - 6)/(x+3) = x - 3 + 3/(x+3), the quotient x - 3 is the slant asymptote)