Question

3. State the amplitude, period and range for each of the following functions.

Answer 1

Given:

There are given the trigonometric function:

`\begin{gathered} \lparen a):f\mleft(x\mright)=-3sin3x \\ \left(b\right):f\mleft(x\mright)=sin((1)/(3)x) \\ (c):f(x)=(1)/(4)cos(0.5x) \end{gathered}`

Step-by-step explanation:

From the equation (a):

The amplitude is defined when displacement or distance is moved by a point from the equilibrium position.

So,

`\begin{gathered} amplitude:3 \\ period:(2\pi)/(3) \\ range:\left\lbrack-3,3\right\rbrack \end{gathered}`

From the function (b):

`\begin{gathered} f\mleft(x\mright)=sin\lparen(1)/(3)x) \\ amplitude:1 \\ period:6\pi \\ range:\left\lbrack-1,1\right\rbrack \end{gathered}`

And,

From the function (c):

`\begin{gathered} f\mleft(x\mright)=(1)/(4)cos\left(0.5x\right) \\ amplitude:(1)/(4) \\ period:12.566 \\ range:\left\lbrack-(1)/(4),(1)/(4)\right? \end{gathered}`