Determine the Domain and the Range of the Function $$f ( x ) = - 4 x ^ { 2 } - 2 x - 8$$

Multiple Choice

Determine the domain and the range of the function.
- $$f ( x ) = - 4 x ^ { 2 } - 2 x - 8$$

A) domain: all real numbers
range: $\left\{ y \mid y \leq - \frac { 31 } { 4 } \right\}$

B) domain: all real numbers
range: $\left\{ y \mid y \leq \frac { 31 } { 4 } \right\}$

C) domain: all real numbers
range: $\left\{ y \mid y \geq - \frac { 31 } { 4 } \right\}$

D) domain: all real numbers
range: $\left\{ y \mid y \geq \frac { 31 } { 4 } \right\}$