Consider the Following Function $$f ( x ) = \left\{ \begin{array} { c c } 3 - x & x < - 1 \\x & - 1 \leq x < 3 \\( x - 3 ) ^ { 2 } & x \geq 3\end{array} \right.$$

question 74

Short Answer

Consider the following function.
$$f ( x ) = \left\{ \begin{array} { c c } 3 - x & x < - 1 \\x & - 1 \leq x < 3 \\( x - 3 ) ^ { 2 } & x \geq 3\end{array} \right.$$
Determine the values of $a$ for which $\lim _ { x \rightarrow a } f ( x )$ exists.

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Definitions:

Linear Association

A relationship between two variables that can be graphically represented with a straight line, indicating a constant rate of increase or decrease between them.

Multiple Regression Model

A method in statistics that relies on various independent variables to anticipate the response of a dependent variable.

Coefficient

A numerical or constant quantity placed before and multiplying the variable in an algebraic expression.

Independent Variable

A variable in an experiment or model that is manipulated or categorized to observe its effect on the dependent variable.