ACT Math Practice Question #2111 (Hard) | Test Citadel
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ACT Math Difficulty: Hard

Digital ACT Math Practice Question #2111

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What are all vertical asymptotes of the rational function $f(x) = \frac{x - 3}{x^2 - 9}$?
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Hole vs Asymptote rule: Factors that cancel completely from the denominator leave holes, NOT vertical asymptotes. Only $(x+3)$ remains $\implies x = -3$.

Masterclass Solution & Distractor Trap Analysis

Factor the denominator: $f(x) = \frac{x - 3}{(x - 3)(x + 3)}$. For $x \ne 3$, $f(x) = \frac{1}{x + 3}$. The factor $(x - 3)$ creates a removable discontinuity (hole) at $x = 3$, while $(x + 3)$ produces a true vertical asymptote at $x = -3$...

Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...

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