How do you find the domain and range of #y = 2x^3 + 8#?

1 Answer
Feb 22, 2018

Answer:

Range: #[-oo, oo]#
Domain: #[-oo, oo]#

Explanation:

Range:
How BIG can #y# be? How SMALL can #y# be?
Because the cube of a negative number is negative and the cube of a positive number is positive, #y# has no limits; therefore, the range is #[-oo, oo]#.

Domain:
How BIG can #x# be so that the function is always defined? How SMALL can #x# be so that the function is always defined?
Note that this function is never undefined because there is no variable in the denominator. #y# is continuous for all values of #x#; therefore, the domain is #[-oo, oo]#.