SAT Math Practice Question #767 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #767

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

The function \( f \) is defined by \( f(x) = \frac{ax^2 + bx - 120}{2x^2 - 14x + 20} \), where \( a \) and \( b \) are constants. The graph of \( y = f(x) \) in the xy-plane has a horizontal asymptote at \( y = 4 \), a removable discontinuity (hole) at \( x = c \), and a vertical asymptote at \( x = 2 \). What is the value of \( a + b + c \)?
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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)

Desmos Tactical Shortcut: Plot the left-hand side and right-hand side as separate equations (e.g. \( y_1 = f(x) \) and \( y_2 = g(x) \)). Click the intersection points directly to read exact coordinates.

Masterclass Solution & Distractor Trap Analysis

This question rigorously tests your comprehensive understanding of rational functions, combining limits, asymptotes, and algebraic factoring into one elegant puzzle. Let's conquer it piece by piece. Step 1: Analyze the denominator. The deno...

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

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