Question

which of the following statements are true? choose three correct answers.
the frequency is $\frac{1}{pi}$
the graph is stretched vertically by a factor of 5.
the graph is stretched horizontally by a factor of 2.
the amplitude is 10
the period is $4pi$

Explanation:

Step1: Identify amplitude

Amplitude = max y-value = $5$

Step2: Calculate period

Distance between peaks: $5\pi - \pi = 4\pi$

Step3: Calculate frequency

Frequency = $\frac{1}{\text{Period}} = \frac{1}{4\pi}$

Step4: Analyze vertical stretch

Standard sine amplitude is 1, here it's 5, so vertical stretch by 5.

Step5: Analyze horizontal stretch

Standard sine period is $2\pi$, new period is $4\pi = 2\times2\pi$, so horizontal stretch by 2.

Answer:

• The graph is stretched vertically by a factor of 5.
• The graph is stretched horizontally by a factor of 2.
• The period is $4\pi$.