The graph of 𝑦=𝐴sin⁡𝐵𝑥 has amplitude =|𝐴| and period =2𝜋𝐵.Group of answer choicesTrueFalse

1. Break Down the Problem

We need to determine if the statement about the graph $y = A \sin(Bx)$ regarding amplitude and period is true or false.

2. Relevant Concepts

• The amplitude of the sine function represented by $y = A \sin(Bx)$ is defined as $|A|$.
• The period of the sine function is calculated using the formula $\text{Period} = \frac{2\pi}{|B|}$.

3. Analysis and Detail

• Amplitude: The amplitude is indeed given by $|A|$.
• Period: The period specified in the statement is $2\pi B$. However, the correct formula is $\frac{2\pi}{|B|}$.

4. Verify and Summarize

Since the period stated in the problem is incorrect, we can conclude that the statement as a whole is false.

Final Answer

False