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M3-036-A09-V04
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F-TF.5
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M3-036-A09-V04
Choose trig functions to model periodic phenomena using amplitude, frequency, and midline.
Find and verify sinusoidal maximum and minimum values
Problem
For \(p(x)~=~-8\cos(x)~+~15\), use the envelope diagram to state the amplitude, midline, maximum, minimum, and range, then verify the midpoint and half-range relationships.
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A
The amplitude is -8, the midline is 15, the maximum is 7, the minimum is 23, and the range is [23, 7]. The midpoint check is (maximum + minimum)/2 = 15, and the half-range check is (maximum - minimum)/2 = -8.
B
The amplitude is 8, the midline is 15, the maximum is 31, the minimum is -1, and the range is [-1, 31]. The midpoint check is (maximum + minimum)/2 = 15, and the half-range check is (maximum - minimum)/2 = 16.
C
The amplitude is 8, the midline is 15, the maximum is 23, the minimum is 7, and the range is [7, 23]. The midpoint check is (maximum + minimum)/2 = 15, and the half-range check is (maximum - minimum)/2 = 8.
D
The amplitude is 8, the midline is 15, the maximum is 7, the minimum is 23, and the range is [23, 7]. The midpoint check is (maximum + minimum)/2 = 15, and the half-range check is (maximum - minimum)/2 = -8.
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Curriculum context
Standard F-TF.5
Category Functions
Domain Trigonometric Functions
Objective Choose trig functions to model periodic phenomena using amplitude, frequency, and midline.
Problem type Find and verify sinusoidal maximum and minimum values
