#### Answer

The function is continuous $ a = -1.$

#### Work Step by Step

By theorem 8 we can write
$\lim\limits_{x \to -1} (x + 2x^{3})^{4}$
as
$(\lim\limits_{x \to -1} (x + 2x^{3}))^{4}$
This is a polynomial so its limit can be evaluated by substitution.
Because it is evaluated by substitution, the value of the function at -1 is equal to the value of the limit at -1 which means that it is continuous.