Final Answer:
1) Amplitude = 3, Period = $2\pi$, Phase Shift = 0, Axis of Oscillation = 0
2) Amplitude = 1, Period = 6, Phase Shift = 0, Axis of Oscillation = 0
3) Amplitude = 3, Period = 10, Phase Shift = 0, Axis of Oscillation = 0
4) Amplitude = 2, Period = 4, Phase Shift = 0, Axis of Oscillation = 0
5) Amplitude = 4, Period = $2\pi$, Phase Shift = 0, Axis of Oscillation = 0
6) No amplitude or period (tan), Phase Shift = 0, Vertical Shift = –3, Asymptotes at $x = \frac{7}{2} + 14k$, $k \in \mathbb{Z}$
7) Amplitude = 1, Period = 12, Phase Shift = 0, Axis of Oscillation = 3
8) No amplitude or period (tan), Phase Shift = 5, Vertical Shift = 0, Asymptotes at $x = 5 + \frac{13}{2} + 13k = \frac{23}{2} + 13k$, $k \in \mathbb{Z}$
9) Amplitude = 1, Period = 12, Phase Shift = 0, Axis of Oscillation = –3
10) Amplitude = 1, Period = 6, Phase Shift = 2, Axis of Oscillation = 0
11) Amplitude = 1, Period = 10, Phase Shift = –4, Axis of Oscillation = 0
12) No amplitude or period (tan), Phase Shift = 0, Vertical Shift = 2, Asymptotes at $x = 5 + 10k$, $k \in \mathbb{Z}$
13) Amplitude = 1, Period = 6, Phase Shift = 1, Axis of Oscillation = –2
14) Amplitude = 2, Period = 12, Phase Shift = 3, Axis of Oscillation = 4
15) No amplitude or period (tan), Phase Shift = 0, Vertical Shift = –5, Asymptotes at $x = \frac{13}{2} + 13k$, $k \in \mathbb{Z}$
16) Amplitude = 3, Period = 10, Phase Shift = 4, Axis of Oscillation = –2
17) Amplitude = 2, Period = 40, Phase Shift = 6, Axis of Oscillation = 3
18) Amplitude = 10, Period = 14, Phase Shift = –4, Axis of Oscillation = –8
19) Amplitude = 4, Period = 18, Phase Shift = –2, Axis of Oscillation = –3
20) No amplitude or period (tan), Phase Shift = –1, Vertical Shift = 2, Asymptotes at $x = -1 + \frac{5}{2} + 5k = \frac{3}{2} + 5k$, $k \in \mathbb{Z}$
Parent Tip: Review the logic above to help your child master the concept of amplitude and period for sine and cosine functions worksheet answers.
