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

Feb 22, 2018

Range: $\left[- \infty , \infty\right]$
Domain: $\left[- \infty , \infty\right]$

#### 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 $\left[- \infty , \infty\right]$.

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 $\left[- \infty , \infty\right]$.