What is the range of #y = 3 cos 4x #?

1 Answer

Answer:

#-3<=y<=3#

Explanation:

The range is the list of all values that you get when applying the domain (the list of all allowable #x# values).

In the equation #y=3cos4x#, it's the number 3 that is the thing that will affect the range (for working with range, we don't care about the 4 - that deals with how often the graph repeats).

For #y=cosx#, the range is #-1<=y<=1#. The 3 will make the maximum and minimum three times bigger, and so the range is:

#-3<=y<=3#

And we can see that in the graph (the two horizontal lines help to show the range maximum and minimum):

graph{(y-3cos(4x))(y-0x+3)(y-0x-3)=0 [-10, 10, -5, 5]}