How do you find the domain and range of #-3 cos x#?

1 Answer
Trevor Ryan.
Dec 30, 2015

Domain = #RR#.
Rangge = #[-3,3]#

Explanation:

Any general cosine graph of the form #y=AsinBx# has amplitude of #A# (maximum vertical displacement from the rest position), and period #T=(2pi)/B# representing the amount of units on the x-axis for 1 complete cycle of the graph to take place.

So in this particular case, #A=-3 and T=2pi#.

So the domain being all possible x-values allowed is all real numbers #RR#, and the range being all possible y-values allowed is all y-values between #-3 and 3#, including the endpoints, ie the closed interval #[-3,3]#.

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