SAT Math Practice Question #340 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #340

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

The function \( g(x) = \frac{ax^2 + bx + c}{2x^2 - 8} \), where \( a, b, \) and \( c \) are constants, has a horizontal asymptote at \( y = 3 \) and vertical asymptotes at \( x = 2 \) and \( x = -2 \). If the graph of \( g(x) \) in the \( xy \)-plane has \( x \)-intercepts at \( (3, 0) \) and \( (5, 0) \), 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

Get ready for a masterclass in rational functions! This question requires synthesizing asymptotes, intercepts, and polynomial structures. Let's break it down piece by piece. Step 1: Analyze the Horizontal Asymptote (HA). For a rational func...

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

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