Find the Constant a Such That the Function $f ( x ) = \left\{ \begin{array} { l l } 6 , & x \leq - 5 \\a x + b , & - 5 < x < 1 \\- 6 , & x \geq 1\end{array} \right.$

question 45

Multiple Choice

Find the constant a such that the function $f ( x ) = \left\{ \begin{array} { l l } 6 , & x \leq - 5 \\a x + b , & - 5 < x < 1 \\- 6 , & x \geq 1\end{array} \right.$
is continuous on the entire real line.

• A) \(a = 2 , b = 0\)
• B) \(a = 2 , b = - 4\)
• C) \(a = - 2 , b = - 4\)
• D) \(a = - 2 , b = 4\)
• E) \(a = 2 , b = 4\)

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Definitions:

Profit Maximizing

A strategy or point where a firm achieves the highest possible profit given its production costs, sales price, and output level.

Monopoly Firm

A company that is the sole provider of a particular product or service in a market, lacking direct competition.

Output Level

This refers to the quantity of goods or services produced by a firm or an economy within a specific period.

Monopolist

A market participant that has exclusive control over the supply of a particular commodity or service, allowing it to influence price and market conditions.