What is the range for the given function? Does the function have a relative minimum? Relative maximum? If yes, what is the value? For what interval(s) is the function increasing? Decreasing? Constant?
a. Range: ( All real numbers ); No relative minimum or maximum; Increasing on ( (-[infinity], +[infinity]) ); Decreasing on ( (-[infinity], +[infinity]) ); Constant on ( (-[infinity], +[infinity]) )
b. Range: ( (-[infinity], +[infinity]) ); Relative minimum at ( x = 0 ), value = 3; No relative maximum; Increasing on ( (0, +[infinity]) ); Decreasing on ( (-[infinity], 0) )
c. Range: ( [3, +[infinity]) ); Relative minimum at ( x = 0 ), value = 3; Relative maximum at ( x = 0 ), value = 3; Increasing on ( (0, +[infinity]) ); Decreasing on ( (-[infinity], 0) )
d. Range: ( (-[infinity], 3] ); Relative minimum at ( x = 0 ), value = 3; Relative maximum at ( x = 0 ), value = 3; Increasing on ( (-[infinity], 0) ); Decreasing on ( (0, +[infinity]) )