Question
The graph of y = sin 4x is shown. What is different about the graph when compared to its parent function y = sin x ? (1 point) Responses The Amplitude The Amplitude The Period The Period The Midline The Midline The Starting Point
Answers
GPT-4o mini
When comparing the graph of \( y = \sin(4x) \) to its parent function \( y = \sin(x) \), the primary difference is **the period**.
The period of the parent function \( y = \sin(x) \) is \( 2\pi \). For the function \( y = \sin(4x) \), the period is calculated by the formula \( \frac{2\pi}{b} \) where \( b \) is the coefficient of \( x \). In this case, \( b = 4 \), so the period is:
\[
\frac{2\pi}{4} = \frac{\pi}{2}
\]
Thus, the graph of \( y = \sin(4x) \) completes its cycles more quickly than \( y = \sin(x) \), indicating a shorter period.
The response is:
- **The Period**
The period of the parent function \( y = \sin(x) \) is \( 2\pi \). For the function \( y = \sin(4x) \), the period is calculated by the formula \( \frac{2\pi}{b} \) where \( b \) is the coefficient of \( x \). In this case, \( b = 4 \), so the period is:
\[
\frac{2\pi}{4} = \frac{\pi}{2}
\]
Thus, the graph of \( y = \sin(4x) \) completes its cycles more quickly than \( y = \sin(x) \), indicating a shorter period.
The response is:
- **The Period**