# How do you graph #y = 2sin(4x) + 1#, by using the period, domain, range and intercepts?

##### 1 Answer

a) In the function

Call the period P.

#P = (2pi)/4#

#P = pi/2#

b) In the function

The maximum is given by

The minimum is given by

Accordingly, the maximum is at

c) We have most of the information needed to graph from the above questions, but I recommend you find the intercepts (the y intercept and a general rule for the x-intercepts.

**y intercept**

**x intercepts**

Due to the periodicity of the sine function,

We have all the information necessary to graph. My grapher won't let me label points, but you can look above and find a good many (using x-intercepts, periodicity, maximums and minimums).

Hopefully this helps!