What is the range of #y = -2 cos 3x#?

1 Answer
Mar 30, 2018

Answer:

#{yinRR|-2<=y<=2}#

Explanation:

We have to know the range of a normal #cos(x)# function and that is 1 and -1

We next have to know what the translation form of cosine graphs looks like

#Acos[B(x-C)]+D#

A~Amplitude, stretches all the y values by A
B~Period, stretches the period by #1/B#
C~ vertical translation, moves the x values across by C
D~ horizontal translation, moves the y values up D

So A and D effect the range and B and C effect the domain

So from this we know the y values have been stretched by -2 so the range becomes -2 and 2

#{yinRR|-2<=y<=2}#