Question

Use the image to answer the question.

A waveform is graphed on a coordinate plane. The x-axis ranges from negative 2 pi to 2 pi in increments of Start Fraction pi over 2 End Fraction. The y-axis ranges from 0 to 2 in increments of 0.5.
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Which of the following options correctly writes an equation for a cosine function, based on the given graph?

(1 point)
Responses

y=cos(x)+1

y equals cosine left parenthesis x right parenthesis plus 1

y=−cos(x)+1

y equals negative cosine left parenthesis x right parenthesis plus 1

y=−cos(x−1)+1

y equals negative cosine left parenthesis x minus 1 right parenthesis plus 1

y=−cos(x)

Answer 1

y = −cos(x) + 1

Reason: the graph has midline y = 1 and amplitude 1, so the form is A cos x + 1 with |A| = 1. Because the graph has a minimum at x = 0 (y = 0) rather than a maximum, the cosine is reflected (A = −1), giving y = −cos(x) + 1.