Discuss the continuity of the function $f$ given by $f(x) = x^{3} + x^{2} - 1$.

(N/A) The function $f(x) = x^{3} + x^{2} - 1$ is a polynomial function.
Polynomial functions are defined for all real numbers $c \in \mathbb{R}$.
The value of the function at $x = c$ is $f(c) = c^{3} + c^{2} - 1$.
Now,we evaluate the limit of the function as $x$ approaches $c$:
$\lim_{x \to c} f(x) = \lim_{x \to c} (x^{3} + x^{2} - 1) = c^{3} + c^{2} - 1$.
Since $\lim_{x \to c} f(x) = f(c)$ for any arbitrary real number $c$,the function $f$ is continuous at every point in its domain.
Therefore,$f$ is a continuous function on the set of all real numbers $\mathbb{R}$.