Asked by cool boy
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A waveform is graphed on a coordinate plane.
Which function is shown on the graph?
A). f (x) = 3 sin (x/2) + 2
B). f (x) = 3 sin (5x/2) - 2
C). f (x) = 5 sin (5x/2) + 2
D). f (x) = 3 sin (5x/2) + 2
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Answer: D) f(x) = 3 sin(5x/2) + 2
Reason: The graph's midline is y = 2 so the vertical shift is +2. The max and min are y = 5 and y = −1, so the amplitude is (5 − (−1))/2 = 3. Count one full cycle on the x‑axis to get the period T = 4π/5, so b satisfies 2π/b = 4π/5 ⇒ b = 5/2. Thus f(x) = 3 sin((5/2)x) + 2.
Reason: The graph's midline is y = 2 so the vertical shift is +2. The max and min are y = 5 and y = −1, so the amplitude is (5 − (−1))/2 = 3. Count one full cycle on the x‑axis to get the period T = 4π/5, so b satisfies 2π/b = 4π/5 ⇒ b = 5/2. Thus f(x) = 3 sin((5/2)x) + 2.
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