For What Value of the Constant $c$ Is the Function $f$ Continuous On

question 60

Short Answer

For what value of the constant $c$ is the function $f$ continuous on $( - \infty , \infty )$ ?
$$f ( x ) = \left\{ \begin{array} { l l l } c x + 5 & \text { for } & x \leq 2 \\c x ^ { 2 } - 5 & \text { for } & x > 2\end{array} \right.$$

Identify and differentiate between totals, averages, distributions, and ratios in various contexts.

Recognize the significance of relative and absolute frequencies in statistical analysis.

Comprehend the use of median to describe the central tendency of a dataset.

Grasp the conceptual underpinnings of statistics in logical reasoning and evidence evaluation.

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Definitions:

Broken Chain

Often symbolizes the disruption or loss of continuity, which can refer to broken social bonds, interrupted traditions, or halted progress.

Property Qualification

A historical requirement that individuals must own a certain amount of property or land to enjoy specific rights, such as voting or holding public office.

Petitions Of Slaves

Historical documents or appeals made by enslaved individuals seeking freedom, justice, or improved conditions.

Natural Rights

Fundamental human rights, often seen as universal and inalienable, such as life, liberty, and property, as conceptualized by philosophers like John Locke.