Question

The values on the x-axis ranges from negative pi to start fraction 5 pi over 2 end fraction in increments of start fraction pi over 2 end fraction. The values on the y-axis range from negative 4 to 4 in increments of 1. The curve passes through the following: left parenthesis negative pi comma 4 right parenthesis, left parenthesis negative start fraction pi over 2 end fraction comma 0 right parenthesis, left parenthesis 0 comma negative 4 right parenthesis, left parenthesis start fraction pi over 2 end fraction comma 0 right parenthesis, left parenthesis pi comma 4 right parenthesis, left parenthesis start fraction 3 pi over 2 end fraction comma 0 right parenthesis, left parenthesis 2 pi comma negative 4 right parenthesis, and left parenthesis start fraction 5 pi over 2 end fraction comma 0 right parenthesis.

Write the equation of the periodic function based on the graph.

(1 point)
Responses

y=−4cosx

y equals negative 4 cosine x

y=−14cosx

y equals negative Start Fraction 1 over 4 End Fraction cosine x

y=4cosx

y equals 4 cosine x

y=−4sinx

y equals negative 4 sine x
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Answer 1

y = −4 cos x

Reason: amplitude 4 and midline 0. At x = 0 the graph is y = −4, which matches −4 cos(0) = −4, and other given points (π/2 → 0, π → 4, etc.) also fit −4 cos x.