Give a Rule for the Piecewise-Defined Function $f ( x ) = \left\{ \begin{array} { l l } - 4 & \text { if } x \leq 1 \\ - 3 & \text { if } x > 1 \end{array} \right.$

question 406

Multiple Choice

Give a rule for the piecewise-defined function. Then give the domain and range.
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• A) \(f ( x ) = \left\{ \begin{array} { l l } - 4 & \text { if } x \leq 1 \\ - 3 & \text { if } x > 1 \end{array} \right.\); Domain: \(( \infty , \infty )\), Range: \(\{ - 4 , - 3 \}\)
• B) \(f ( x ) = \left\{ \begin{array} { l l } - 4 & \text { if } x < 1 \\ - 3 & \text { if } x \geq 1 \end{array} \right.\); Domain: \(\{ - 4 , - 3 \}\), Range: \(( \infty , \infty )\)
• C) \(f ( x ) = \left\{ \begin{array} { l l } - 4 & \text { if } x < 1 \\ - 3 & \text { if } x \geq 1 \end{array} \right.\); Domain: \(( \infty , \infty )\), Range: \(\{ - 4 , - 3 \}\)
• D) \(f ( x ) = \left\{ \begin{array} { l l } - 4 & \text { if } x \leq 1 \\ - 3 & \text { if } x > 1 \end{array} \right.\); Domain: \(\{ - 4 , - 3 \}\), Range: \(( \infty , \infty )\)

Recognize events within a probability context and classify them as simple, compound, independent, or dependent.

Distinguish between mutually exclusive and collectively exhaustive events.

Compute probabilities applying appropriate probability rules.

Understand the concept of conditional probability and its calculation.

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Definitions:

AntiAromatic

Compounds that have conjugated pi electron systems with 4n pi electrons, which destabilize the molecule, making it less stable than if the pi electrons were localized.

NonAromatic

Refers to organic compounds that do not possess the special stability associated with cyclic, planar systems that follow Huckel’s rule of delocalized electrons.

π Network

A system of conjugated pi bonds within a molecule that allows for the delocalization of pi electrons across all the adjacent aligned p orbitals.

Extremely Slow Rate

Describes a process or reaction that proceeds at a very slow pace, often due to kinetic barriers or unfavorable conditions.