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

question 68

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: \(\left\{ \mathrm { y } \mid \mathrm { y } \leq \frac { 31 } { 4 } \right\}\)
• C) domain: all real numbers
• range: \(\left\{ y \mid y \geq - \frac { 31 } { 4 } \right\}\)
• D) domain: all real numbers
• range: \(\left\{ y \mid y \geq \frac { 31 } { 4 } \right\}\)

---

Definitions:

Total Revenue

The overall amount of money generated by a business from selling its goods or services before any costs are subtracted.

Elastic Than Industry

A condition or scenario where a particular firm or product has a higher sensitivity to price changes compared to the overall industry.

Monopolist

A single seller in a market, possessing significant market power, and facing little to no competition in offering a unique product or service.

Elastic Segment

A section of the demand curve where consumers are highly responsive to changes in price, indicating elasticity of demand.