Question

The waveform passes through coordinates left parenthesis negative 2 pi comma 0 right parenthesis, left parenthesis Start Fraction negative 3 pi over 2 End Fraction comma 0 right parenthesis, left parenthesis negative pi comma 0 right parenthesis, left parenthesis Start Fraction negative pi over 2 End Fraction comma 0 right parenthesis, left parenthesis 0 comma 0 right parenthesis, left parenthesis Start Fraction pi over 2 End Fraction comma 0 right parenthesis, left parenthesis pi comma 0 right parenthesis, left parenthesis Start Fraction 3 pi over 2 End Fraction comma 0 right parenthesis, and left parenthesis 2 pi comma 0 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 a frequency of 1.
The graph has a frequency of 1.

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

The graph has a period of π2
.
The graph has a period of Start Fraction pi over 2 End Fraction .

The graph has a period of π
.

Answer 1

Zeros occur every π/2, so the function behaves like sin(2x). That gives

- Period = 2π/2 = π (so the statement "The graph has a period of π." is correct).
- Frequency = 1/period = 1/π (so "frequency of 1" is incorrect).
- Amplitude cannot be deduced from the zeros alone (but "amplitude of 2" is incorrect unless peaks at ±2 are shown).

Therefore the correct choice is: The graph has a period of π.