SOLUTION: Which function has a period of 4? Link below to the function copy and paste link please, thank you!! Link : http://prntscr.com/b7v639

Algebra ->  Trigonometry-basics -> SOLUTION: Which function has a period of 4? Link below to the function copy and paste link please, thank you!! Link : http://prntscr.com/b7v639      Log On


   

Question 1035742: Which function has a period of 4?
Link below to the function copy and paste link please,
thank you!!
Link : http://prntscr.com/b7v639
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

(A)                 (B)
      

The period of a function is the number of units along the x-axis
that span one complete cycle of the graph, where one complete
cycle is either
graph%2850%2C50%2C10%2C18%2C6%2C14%2C-4sin%28pi%2F4%2A%28x-10%29%29%2B10%29%29 or graph%2850%2C50%2C10%2C18%2C6%2C14%2C4sin%28pi%2F4%2A%28x-10%29%29%2B10%29%29 or graph%2850%2C50%2C10%2C18%2C6%2C14%2C4cos%28pi%2F4%2A%28x-10%29%29%2B10%29%29 or graph%2850%2C50%2C10%2C18%2C6%2C14%2C-4cos%28pi%2F4%2A%28x-10%29%29%2B10%29%29

As you see in the first graph (A), the cycle graph%2850%2C50%2C10%2C18%2C6%2C14%2C-4sin%28pi%2F4%2A%28x-10%29%29%2B10%29%29begins at -4 on
the x-axis and the cycle doesn't end until +4 on the x axis.
From -4 to +4 on the x-axis is a span of (+4)-(-4) = +4+4 = 8
units, so the period of the (A) graph is 8.

On graph (B), there are two complete cycles like this graph%2850%2C50%2C10%2C18%2C6%2C14%2C4sin%28pi%2F4%2A%28x-10%29%29%2B10%29%29 
over the same span on the x-axis. Therefore the number of units on the 
x-axis that is spanned by just one cycle graph%2850%2C50%2C10%2C18%2C6%2C14%2C4sin%28pi%2F4%2A%28x-10%29%29%2B10%29%29 is 4.
So the period of the (B) graph is 4.

Edwin