Question

Explain how to find the period and the critical points (Zeros, Maximums, Minimums, Asymptotes) of y= -cos(3x)+1

Answer 1

Expalantion:

The function is goiven below as

`y=-cos(3x)+1`

The graph is given below as

Step 1:

To figure out the period of the cosine function, we will use the relation below

`\begin{gathered} (2\pi)/(B) \\ where, \\ B=3 \end{gathered}`

Hence,

The period will be

`(2\pi)/(3)`

The minimum points is given below as

`\mathrm{Minimum}\left((2\pi )/(3)n,\:0\right)`

The maximum points is given below as

`\mathrm{Maximum}\left((\pi )/(3)+(2\pi )/(3)n,\:2\right)`

It has NO ASYMPTOTES

The y-intercept is given below as

`\:\mathrm{Y\:Intercepts}:\:\left(0,\:0\right)`

The zeros is given below as

`\mathrm{X\:Intercepts}:\:\left((2\pi n)/(3),\:0\right)`