Question

The waveform passes through coordinates left parenthesis Start Fraction negative 3 pi over 2 End Fraction comma negative 2 right parenthesis, left parenthesis Start Fraction negative pi over 2 End Fraction comma 6 right parenthesis, left parenthesis Start Fraction pi over 2 End Fraction comma negative 2 right parenthesis, and left parenthesis Start Fraction 3 pi over 2 End Fraction comma 6 right parenthesis.

Identify the amplitude, period, and frequency of the graphed function. Which of these statements about the function is correct?

(1 point)
Responses

The graph has an amplitude of 6.
The graph has an amplitude of 6.

The graph has an amplitude of 2.
The graph has an amplitude of 2.

The graph has a frequency of 12π
.
The graph has a frequency of 1 over 2 pi .

The graph has a period of 1.

Answer 1

Amplitude = 4, Period = 2π, Frequency = 1/(2π).

Reason: midline = (6 + (−2))/2 = 2 so amplitude = 6 − 2 = 4. Peaks repeat every 2π (e.g. −π/2 to 3π/2), so period = 2π and frequency = 1/(2π).

Thus the only correct choice given is: "The graph has a frequency of 1 over 2π."