Given the equation \( y=2 \tan (3 x-21) \) The period is: The horizontal shift is: \( \square \) units to the Select an answer \( \boldsymbol{\square} \)

To analyze the equation \( y = 2 \tan(3x - 21) \), we need to determine the period and the horizontal shift. 1. **Period**: The standard period of the tangent function \( \tan(kx) \) is given by \( \frac{\pi}{|k|} \). In this case, \( k = 3 \). Therefore, the period is: \[ \text{Period} = \frac{\pi}{|3|} = \frac{\pi}{3} \] 2. **Horizontal Shift**: The general form of the tangent function is \( y = a \tan(b(x - c)) \), where \( c \) represents the horizontal shift. In our equation, we can rewrite it as: \[ y = 2 \tan(3(x - 7)) \] Here, we can see that \( 3x - 21 = 3(x - 7) \), which indicates a horizontal shift of \( 7 \) units to the right (since \( c = 7 \)). Thus, we can summarize the results as follows: - The period is \( \frac{\pi}{3} \). - The horizontal shift is \( 7 \) units to the right. So, the final answers are: - The period is: \( \frac{\pi}{3} \) - The horizontal shift is: \( 7 \) units to the **right**.