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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.

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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 #410

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{ax + b}{cx + d} $, where $ a, b, c, $ and $ d $ are constants. In the $ xy $-plane, the graph of $ y = f(x) $ has a horizontal asymptote at $ y = 2 $, a vertical asymptote at $ x = -3 $, and passes through the point $ (1, 4) $. The function $ g $ is defined such that its graph is the reflection of the graph of $ f $ across the line $ y = x $. What is the value of $ g(4) $?

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 is a spectacular test of conceptual understanding over brute force. You can solve this in 5 minutes with heavy algebra, or in 5 seconds if you know your 800-level function properties. Let's start with the conceptual shortcut, which is ...

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

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