How does Test Citadel mirror the real Digital SAT Bluebook exam?

Test Citadel features an authentic Bluebook-calibrated countdown timer with visibility toggle, question navigation grid, choice eliminator cross-out tool, embedded Desmos graphing calculator, and official College Board formula sheets.

Can I try Test Citadel questions for free?

Yes. Every visitor can complete 4 free diagnostic problems (2 Math with Desmos and 2 Reading & Writing) with full Socratic explanations before upgrading to Citadel Pro.

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Citadel Pro grants unlimited access to 2,600+ adaptive questions, multi-tier Socratic hint trees, Desmos graphing shortcuts, distractor trap breakdowns, and simulated full-length SAT and ACT exams.

SAT Math Difficulty: Hard (800) • Calibrated to 2026 Testing Standard

Digital SAT Math Practice Question #388

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 + b}{cx + d} $, where $ a $, $ b $, $ c $, and $ d $ are non-zero constants. The graph of $ y = f(x) $ in the xy-plane has a vertical asymptote at $ x = 3 $ and a horizontal asymptote at $ y = 2 $. If $ f(1) = 0 $, what is the value of $ \frac{b}{d} $?

Select Your Answer:

Socratic AI Engine Step-by-Step Derivation

0ms Precomputed

Tactical Insight (Hint 1)

Check for special right triangles ($ 30^\circ-60^\circ-90^\circ $ or $ 45^\circ-45^\circ-90^\circ $) or the complementary angle identity $ \sin(x) = \cos(90^\circ - x) $.

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 problem tests your mastery of rational functions and how their equations translate into graphical features. We need to decode three distinct pieces of information into algebraic equations linking $ a, b, c, $ and $ d $. Clue 1: Ver...

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

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