Question

1) State the amplitude, period, phase shift, vertical shift and graph

Answer 1

Answer:

See answers and explanations below (along with a visual graph)

Step-by-step explanation:

For the function $y=acos(b(x+c))+d$:

Amplitude: $|a|$

Period: $\frac{2\pi}{|b|}$

Phase shift: $\frac{-c}{b}$

Vertical shift: $d$

Therefore, for $y=2cos(\frac{2}{3}(\theta+\pi))-1$:

Amplitude: $|a|=|2|=2$, which is 2 units above and below the midline (see d)

Period: $\frac{2\pi}{|b|}=\frac{2\pi}{|\frac{2}{3}|}=\frac{2\pi}{\frac{2}{3}}=3\pi$, so the cycle will repeat every 3π units

Phase shift: $\frac{-c}{b}=\frac{-\frac{2\pi}{3} }{\frac{2}{3} }=-\pi$, or π units to the left

Vertical shift: $d=-1$, or 1 unit down