The range of a function is the set of values between the maximum and minimum values that a certain function can output for its domain. The domain of a function is all the function input values that will produce a valid output value.
The standard range of cos(theta) = [-1,1] and the domain: (-oo,oo). In other words, the maximum value of cos(theta) is 1, the minimum value is -1, and all numbers can be plugged into cos(theta) and a valid function value will be found. By multiplying cos(theta) by -3, all values of cos(theta) will be inverted because of the negative sign, and all values will be increased by a factor of 3 as well.
cos(0) = 1 (maximum value)
-3(cos(0)) = -3 (1) = -3 (new minimum value)
Multiplying cos(theta) by a factor of -3 does not affect the set of valid numbers that can be entered into cos(theta) where a valid function value can be found, so the domain of -3cos(theta) is the same as cos(theta).
