y=2cos2x. find the domain,range,amplitude, and period.

Question

y=2cos2x.what is the

 

domain=?

range=?

amplitude=?

period=?

Answer 1

A cosine function is continuous for all values of x.  Domain is all real numbers.

A trig function's range is determined by its amplitude.

 

Range in the interval (-amplitude, amplitude)

 

The period is the time frame it takes the function to complete one cycle.  In other words, when does the graph revisit its starting peak?  You can calculate the period by dividing 2π by the frequency.  The frequency of the function is 2.  Therefore, the period is π.