9. = 4sin(πx + 2) − 5 y Amplitude: = 4 = 4 A Period: = = = 2π 2π 2 T ω π φ Phase Shift: = − 2 = − 2 ω π π Interval defining one cycle: φ φ ⎡ , + ⎤ = ⎡− 2 , 2 − 2 ⎤ T ω ⎢ω π π ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ Subinterval width: = 2 = 1 T 4 4 2 = 3cos(πx − 2) + 5 11. y Key points: ⎛ − 2 , −5 ⎞ , ⎛ 1 − 2 , −1⎞ , ⎛1 − 2 , Amplitude: = 3 = 3 A −5 ⎞ , 2π 2π π ⎜ ⎟ Period: = = = 2 T ⎜ π ⎟ ⎜ π ⎟ 2 ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ω π ⎛ 3 − 2 , −9 ⎞ , ⎛ 2 − 2 , φ 2 −5 ⎞ π ⎜ 2 π ⎟ ⎜ ⎟ Phase Shift: = ⎝ ⎠ ⎝ ⎠ ω π Interval defining one cycle: φ φ ⎡ , + ⎤ = ⎡ 2 , 2 + 2 ⎤ T ω ⎢ω ⎥ ⎢π π ⎥ ⎣ ⎦ ⎣ ⎦ Subinterval width: = 2 = 1 T 4 4 2 Key points: ⎞ ⎛ 2 ,8 ⎞ , ⎛ 1 2 ,5 , , + ,5 , 2 , ⎜1 + ⎟ ⎛ 3 2 π π ⎜ ⎟ ⎜ 2 ⎟ π π ⎟ 2 ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎛ 2 + 2 , 8 ⎞ π ⎜ ⎟ 10. ⎝ ⎠ = 2 cos(2πx + 4) + 4 y Amplitude: = 2 = 2 A Period:
9. y = 4sin(πx + 2) − 5 Amplitude: A = 4 = 4 Period: T = 2π = 2π = 2 ω π Phase Shift: φ = ω − 2 = − 2 π π Interval defining one cycle: ⎡ φ , φ + T ⎤ = ⎡− 2 , 2 − 2 ⎤ ⎢ω ω ⎥ ⎢ π π ⎥ ⎣ ⎦ ⎣ ⎦ Subinterval width: T = 2 = 1 4 4 2 11. y = 3cos(πx − 2) + 5 Key points: ⎛ − 2 , −5 ⎞ , ⎛ 1 − 2 , −1⎞ , ⎛1 − 2 , −5 ⎞ , Amplitude: A = 3 = 3 2π 2π ⎜ π ⎟ ⎜ 2 π ⎟ ⎜ π ⎟ Period: T = = = 2 ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ω π ⎛ 3 − 2 , −9 ⎞ , ⎛ 2 − 2 , −5 ⎞ φ 2 ⎜ 2 π ⎟ ⎜ π ⎟ Phase Shift: = ⎝ ⎠ ⎝ ⎠ ω π Interval defining one cycle: ⎡ φ , φ + T ⎤ = ⎡ 2 , 2 + 2 ⎤ ⎢ω ω ⎥ ⎢π π ⎥ ⎣ ⎦ ⎣ ⎦ Subinterval width: T = 2 = 1 4 4 2 Key points: ⎞ ⎛ 2 ,8 ⎞ , ⎛ 1 2 ,5 , ⎜1 + ⎛ 3 2 , 2 ⎟ , + ,5 , ⎜ π ⎟ 2 π ⎟ π ⎜ 2 π ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎛ 2 + 2 , 8 ⎞ ⎜ π ⎟ 10. ⎝ ⎠ y = 2 cos(2πx + 4) + 4 Amplitude: A = 2 = 2 Period:
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