Questions: Consider the following. Consider the following. y = 4 sin(3x) + 3 Find the period and the amplitude of the graph period amplitude Consider one cycle beginning on the y-axis. Divide smallest x-value (x, y) = ( ) (x, y) = ( , y) = ( ) (x, y) = ( ) largest x-value (x, y) = ( )

Consider the following. Consider the following. y = 4 sin(3x) + 3 Find the period and the amplitude of the graph period amplitude Consider one cycle beginning on the y-axis. Divide smallest x-value (x, y) = ( ) (x, y) = ( , y) = ( ) (x, y) = ( ) largest x-value (x, y) = ( )
Transcript text: Consider the following. \[ \begin{array}{l} \text { Consider the following. } \\ \qquad y=4 \sin (3 x)+3 \\ \text { Find the period and the amplitude of the graph } \\ \text { period } \\ \text { amplitude } \\ \text { Consider one cycle beginning on the } y \text {-axis. Divide } \\ \text { smallest } x \text {-value }(x, y)=(\square) \\ \qquad(x, y)=(\square, y)=(\square) \\ \qquad(x, y)=(\square) \end{array} \] largest $x$-value $\quad(x, y)=($
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Solution

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Solution Steps

Step 1: Identify the function components

The given function is \( y = 4 \sin(3x) + 3 \).

Step 2: Determine the amplitude

The amplitude of a sine function \( y = A \sin(Bx + C) + D \) is given by the absolute value of \( A \). Here, \( A = 4 \).

Step 3: Determine the period

The period of a sine function \( y = A \sin(Bx + C) + D \) is given by \( \frac{2\pi}{|B|} \). Here, \( B = 3 \), so the period is \( \frac{2\pi}{3} \).

Final Answer

  • Period: \( \frac{2\pi}{3} \)
  • Amplitude: 4
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