SAT Math Practice Question #885 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #885

Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.

The rational function \( f \) is defined by: \[ f(x) = \frac{2x^2 + ax - 12}{x^2 - 9} \] where the coefficient in the numerator is a constant. If \( f \) has a removable discontinuity (hole) at \( x = 3 \), what is the value of \( \lim_{x \to 3} f(x) \)?
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Socratic AI Engine Step-by-Step Derivation
0ms Precomputed
Tactical Insight (Hint 1)

A hole occurs where a factor \( (x - c) \) cancels from both the numerator and denominator. Substitute \( x = 3 \) into the numerator to find the missing constant.

Elimination Framework (Hint 2)

Desmos Shortcut: Enter \( f(x) \) into Desmos with a slider for the unknown constant. Slide it until the graph shows an open circle at \( x = 3 \) rather than a vertical asymptote!

Masterclass Solution & Distractor Trap Analysis

For \( f(x) \) to possess a removable discontinuity at \( x = 3 \), the numerator must also have \( (x - 3) \) as a factor. Setting the numerator equal to 0 at \( x = 3 \) reveals the unknown coefficient. Factoring both the numerator and de...

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

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