What is the domain and range of #K(t) = 6cos (90t) - 10#?

1 Answer
Jun 6, 2016

Answer:

Domain: all real numbers.
Range: #[-16,-4]#.

Explanation:

The domain of a function #cos(x)# is all real numbers. Therefore, the domain of function #K(t)=6cos(90t)-10# is a set of all real numbers.

The range of function #cos(x)# is #[-1,1]#.
Therefore, the range of #cos(90t)# is the same #[-1,1]#.
Multiplication of this by #6# transforms the range to #[-6,6]#.
Subtraction of #10# from #6cos(90t)# shifts the range down by #10#, so it becomes #[-16,-4]#.