Evaluate the piecewise defined function at the indicated...

Evaluate the piecewise defined function at the indicated values. $$ \begin{array}{ll}{f(x)=\left\{\begin{array}{ll}{x^{2}+2 x} & {\text { if } x \leq-1} \\ {x} & {\text { if }-1<x \leq 1} \\ {-1} & {\text { if } x>1}\end{array}\right.} \\ {f(-4), f\left(-\frac{3}{2}\right), f(-1), f(0), f(25)}\end{array} $$

Evaluate the piecewise defined function at the indicated values.
$$
\begin{array}{ll}{f(x)=\left\{\begin{array}{ll}{x^{2}+2 x} & {\text { if } x \leq-1} \\ {x} & {\text { if }-1<x \leq 1} \\ {-1} & {\text { if } x>1}\end{array}\right.} \\ {f(-4), f\left(-\frac{3}{2}\right), f(-1), f(0), f(25)}\end{array}
$$

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Key Concepts

Function Evaluation

Evaluating a function involves substituting a specific input value into the function's rule to compute the output. When dealing with piecewise functions, the evaluation process includes first determining which expression or rule applies to the given input based on the function's defined intervals.

Domain Partitioning and Boundary Conditions

Domain partitioning refers to dividing the overall input domain into sections based on given inequalities, where each section has its own functional rule. Understanding boundary conditions is crucial because they determine which rule applies when an input value lies exactly at the border between intervals. Clarity in these cases ensures accurate evaluation of the function.

Piecewise Functions

Piecewise functions are defined by different expressions over distinct intervals of the domain. This concept allows a function to have multiple behaviors depending on the input values, which is common in real-world applications where a problem may naturally split into cases. Each piece of the function comes with its own rule that is valid only within a specific portion of the function's domain.

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