Question

match each function in column i with the appropriate description in column ii. amplitude = 3, period = \frac{2\pi}{5}, phase shift = \frac{2}{5} amplitude = 3, period = \pi, phase shift = \frac{5}{2} amplitude = 2, period = \frac{2\pi}{3}, phase shift = \frac{5}{3} amplitude = 5, period = \pi, phase shift = \frac{3}{2} drag each description above to match the function below. i ii 19. y = 2 sin(3x - 5) 20. y = 3 sin(2x - 5) 21. y = - 5 sin(2x - 3) 22. y = - 3 sin(5x - 2)

Explanation:

Step1: Recall sine - function formula

The general form of a sine function is $y = A\sin(Bx - C)+D$. The amplitude is $|A|$, the period is $T=\frac{2\pi}{|B|}$, and the phase - shift is $\frac{C}{B}$.

Step2: Analyze $y = 2\sin(3x - 5)$

For $y = 2\sin(3x - 5)$, $A = 2$, $B = 3$, $C = 5$. Amplitude $|A|=2$, period $T=\frac{2\pi}{|B|}=\frac{2\pi}{3}$, phase - shift $\frac{C}{B}=\frac{5}{3}$.

Step3: Analyze $y = 3\sin(2x - 5)$

For $y = 3\sin(2x - 5)$, $A = 3$, $B = 2$, $C = 5$. Amplitude $|A| = 3$, period $T=\frac{2\pi}{|B|}=\pi$, phase - shift $\frac{C}{B}=\frac{5}{2}$.

Step4: Analyze $y=-5\sin(2x - 3)$

For $y=-5\sin(2x - 3)$, $A=-5$, $B = 2$, $C = 3$. Amplitude $|A| = 5$, period $T=\frac{2\pi}{|B|}=\pi$, phase - shift $\frac{C}{B}=\frac{3}{2}$.

Step5: Analyze $y=-3\sin(5x - 2)$

For $y=-3\sin(5x - 2)$, $A=-3$, $B = 5$, $C = 2$. Amplitude $|A| = 3$, period $T=\frac{2\pi}{|B|}=\frac{2\pi}{5}$, phase - shift $\frac{C}{B}=\frac{2}{5}$.

Answer:

1. amplitude = 2, period = $\frac{2\pi}{3}$, phase shift = $\frac{5}{3}$
2. amplitude = 3, period = $\pi$, phase shift = $\frac{5}{2}$
3. amplitude = 5, period = $\pi$, phase shift = $\frac{3}{2}$
4. amplitude = 3, period = $\frac{2\pi}{5}$, phase shift = $\frac{2}{5}$