Given:
There are given the trigonometric function:
[tex]\begin{gathered} \lparen a):f\mleft(x\mright)=-3sin3x \\ \left(b\right):f\mleft(x\mright)=sin(\frac{1}{3}x) \\ (c):f(x)=\frac{1}{4}cos(0.5x) \end{gathered}[/tex]Explanation:
From the equation (a):
The amplitude is defined when displacement or distance is moved by a point from the equilibrium position.
So,
[tex]\begin{gathered} amplitude:3 \\ period:\frac{2\pi}{3} \\ range:\left\lbrack-3,3\right\rbrack \end{gathered}[/tex]From the function (b):
[tex]\begin{gathered} f\mleft(x\mright)=sin\lparen\frac{1}{3}x) \\ amplitude:1 \\ period:6\pi \\ range:\left\lbrack-1,1\right\rbrack \end{gathered}[/tex]And,
From the function (c):
[tex]\begin{gathered} f\mleft(x\mright)=\frac{1}{4}cos\left(0.5x\right) \\ amplitude:\frac{1}{4} \\ period:12.566 \\ range:\left\lbrack-\frac{1}{4},\frac{1}{4}\right? \end{gathered}[/tex]