SAT Math Practice Question #598 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #598

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

The rational function \( f(x) = \frac{ax^2 + bx + c}{3x^2 + dx - 6} \), where \( a, b, c, \) and \( d \) are constants, has a horizontal asymptote at \( y = 4 \), a vertical asymptote at \( x = 2 \), and a removable discontinuity (a hole) at \( x = -1 \). Additionally, \( f(x) \) has an \( x \)-intercept at \( x = 3 \). What is the value of \( a + b + c + d \)?
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Socratic AI Engine Step-by-Step Derivation
0ms Precomputed
Tactical Insight (Hint 1)

Identify the quadratic form: consider converting to vertex form \( y = a(x-h)^2 + k \) or using \( x = - rac{b}{2a} \) to find the line of symmetry.

Elimination Framework (Hint 2)

Elimination Shortcut: Check the extremes or test answer choices starting with C to binary search the correct magnitude.

Masterclass Solution & Distractor Trap Analysis

This is a brilliantly complex rational functions problem that tests your ability to reverse-engineer an equation from its graphical features. Let's build the function step-by-step. Step 1: Horizontal Asymptote (HA). The degrees of the numer...

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

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