SAT Math Practice Question #338 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #338

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

The function \( f(x) = c \cdot d^x \) is defined such that \( c \) and \( d \) are positive constants. If \( f(x+3) = 64 \cdot f(x) \) for all real values of \( x \), and the graph of \( y = f(x) \) in the \( xy \)-plane passes through the point \( (2, 80) \), what is the value of \( f(-1) \)?
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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 question is testing your deep understanding of exponential function transformations and exponent rules. Step 1: Unpack the transformation equation. We are given the core rule: \( f(x+3) = 64 \cdot f(x) \). Let's plug our function defin...

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

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