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AP Precalculus -3.1 Periodic Phenomena- MCQ Exam Style Questions - Effective Fall 2023

AP Precalculus -3.1 Periodic Phenomena- MCQ Exam Style Questions – Effective Fall 2023

AP Precalculus -3.1 Periodic Phenomena- MCQ Exam Style Questions – AP Precalculus- per latest AP Precalculus Syllabus.

AP Precalculus – MCQ Exam Style Questions- All Topics

Question 

 
 
 
 
 
 
 
 
 
 
 
 
Let \( f \) be a sinusoidal function. The graph of \( y = f(x) \) is given in the \( xy \)-plane. What is the period of \( f \)?
(A) 2
(B) 3
(C) 4
(D) 6
▶️ Answer/Explanation
Detailed solution

The period of a sinusoidal function is the horizontal distance between consecutive points at which the pattern repeats (e.g., from peak to peak or trough to trough). From the given graph, consecutive maxima occur at \( x = 1 \) and \( x = 5 \), and consecutive minima occur at \( x = -1 \) and \( x = 3 \). Thus, the period is \( 5 – 1 = 4 \) (or \( 3 – (-1) = 4 \)).
✅ Answer: (C)

Question 

 
 
 
 
 
 
 
 
 
 
 
Let \( f \) be a sinusoidal function. The graph of \( y = f(x) \) is given in the \( xy \)-plane. What is the period of \( f \)?
(A) 2
(B) 3
(C) 4
(D) 6
▶️ Answer/Explanation
Detailed solution

The period is the horizontal distance after which the graph repeats itself. From the given graph description (and typical sinusoidal graph shown in original problem):
• Maxima occur at \( x = 1 \) and \( x = 5 \), so the horizontal distance between consecutive maxima is \( 5 – 1 = 4 \).
• Minima occur at \( x = -1 \) and \( x = 3 \), distance \( 3 – (-1) = 4 \).
Thus, the period is 4.
✅ Answer: (C)

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