determine the amplitude and period of the function. graph the function. y = - 3 cos 4/3 x

Explanation:

Step1: Recall amplitude formula

For a cosine function of the form $y = A\cos(Bx)$, the amplitude is given by $|A|$. In the function $y=- 3\cos(\frac{4}{3}x)$, $A = - 3$.

Step2: Calculate amplitude

$|A|=|-3| = 3$.

Step3: Recall period formula

The period of a cosine function $y = A\cos(Bx)$ is $T=\frac{2\pi}{|B|}$. Here, $B=\frac{4}{3}$.

Step4: Calculate period

$T=\frac{2\pi}{\left|\frac{4}{3}\right|}=\frac{2\pi}{\frac{4}{3}}=\frac{3\pi}{2}$.

Answer:

Amplitude: $3$; Period: $\frac{3\pi}{2}$