Question

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

Answer 1

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]`.