Question

name:____________________ test

1. $y = 2\cos(x - \frac{\pi}{4}) - 1$
2. $y = \tan(\pi x - \frac{\pi}{2})$
3. $y = -\csc(\frac{\pi}{3}x - \pi) + 1$
4. $y = -2\sin(\frac{x}{2} + \frac{\pi}{4})$
5. $y = 4\sec(x + \frac{\pi}{2}) - 3$

Explanation:

Answer:

1. Amplitude: \( 2 \); Period: \( 2\pi \); Phase Shift: \( \frac{\pi}{4} \) (to the right); Vertical Shift: \( - 1 \)
2. Amplitude: N/A (for tangent function); Period: \( 1 \); Phase Shift: \( \frac{1}{2} \) (to the right); Vertical Shift: \( 0 \)
3. Amplitude: N/A (for cosecant function); Period: \( 6 \); Phase Shift: \( 3 \) (to the right); Vertical Shift: \( 1 \)
4. Amplitude: \( 2 \); Period: \( 4\pi \); Phase Shift: \( -\frac{\pi}{2} \) (to the left); Vertical Shift: \( 0 \)
5. Amplitude: N/A (for secant function); Period: \( 2\pi \); Phase Shift: \( -\frac{\pi}{2} \) (to the left); Vertical Shift: \( - 3 \)