Find the vertical and horizontal asymptotes of the rational function: f(x) = (3x + 6) / (x - 4).
Answer and explanation
Correct answer: C. Vertical: x = 4, Horizontal: y = 3
- Step 1: Vertical asymptote occurs where denominator is zero and numerator is non-zero: x - 4 = 0 => x = 4.
- Step 2: Horizontal asymptote for rational functions of equal degree is the ratio of leading coefficients: y = 3/1 = 3.
Answer
Vertical: x = 4, Horizontal: y = 3.
Why not the others: Option 'Vertical: x = -2, Horizontal: y = 3' confuses the x-intercept (-2, 0) with a vertical asymptote. Option 'Vertical: x = 4, Horizontal: y = 6' takes the constant term ratio instead of leading coefficients. Option 'Vertical: x = -4, Horizontal: y = 3' has a sign error in the vertical asymptote.
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