Question

b. $y = \frac{1}{3}\tan 6x - 2$

amplitude vertical shift
period phase shift
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Explanation:

Step1: Identify tangent function form

The general form is $y = A\tan(Bx - C) + D$, where for $y=\frac{1}{3}\tan 6x - 2$, $A=\frac{1}{3}$, $B=6$, $C=0$, $D=-2$.

Step2: Determine amplitude

Tangent functions have no defined amplitude (they have no maximum/minimum finite values).

Step3: Calculate period

Period of tangent is $\frac{\pi}{|B|}$.
$\text{Period} = \frac{\pi}{6}$

Step4: Find vertical shift

Vertical shift is $D$.
$\text{Vertical Shift} = -2$ (2 units downward)

Step5: Find phase shift

Phase shift is $\frac{C}{B}$.
$\text{Phase Shift} = \frac{0}{6} = 0$

Answer:

Amplitude	Vertical Shift
Period	Phase Shift
$\frac{\pi}{6}$	$0$