What is the range of y = -2 cos 3xy=−2cos3x?

1 Answer
Rohan N.
Mar 30, 2018

{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}

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