What are all the vertical and horizontal asymptotes of the rational function ?

Answer and explanation

Correct answer: B. Vertical: ; Horizontal:

  1. Step 1: Factor numerator and denominator: .
  2. Step 2: Cancel common factor for : this creates a removable discontinuity (hole) at , not a vertical asymptote.
  3. Step 3: The remaining factor in denominator yields a vertical asymptote at .
  4. Step 4: For horizontal asymptote, compute limit as : , so .
Answer
Vertical: x = 3; Horizontal: y = 3.
Why not the others: The option with vertical asymptotes incorrectly includes as an asymptote rather than a hole; the option with and has incorrect slope ratio; the option with horizontal asymptote has horizontal asymptote at 0.

Practise more Functions, Calculus, Vectors and Analytic Geometry.

Free questions with an explanation for every one, and full timed Tahsili SAAT (Saudi Arabia) mock tests.