For each piecewise function, find the specified function...

For each piecewise function, find the specified function values.
$$
\begin{array}{l}
f(x)=\left\{\begin{array}{ll}
3, & \text { for } x \leq-2, \\
\frac{1}{2} x+6, & \text { for } x>-2
\end{array}\right. \\
f(-5), f(-2), f(0), \text { and } f(2)
\end{array}
$$

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Key Concepts

Piecewise Functions

A piecewise function is a function defined by different expressions over different parts of its domain. Each expression is applied to its corresponding subdomain, making it necessary to consider the condition associated with each segment when evaluating the function.

Domain Partitioning and Case Conditions

In problems involving piecewise functions, the domain is partitioned into intervals or segments where different rules or formulas apply. To correctly evaluate the function at a certain point, one must identify which domain segment that point falls into based on the provided conditions.

Function Evaluation

Function evaluation involves substituting a specific value into the appropriate expression of the function. When dealing with piecewise functions, it is important first to determine which case applies for the input value before performing the substitution and computation.

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