A function that is defined by two or more different subfunctions is **piecewise-defined**. Each subfunction applies on its own portion of the piecewise-defined function’s domain (or, its own subdomain).

In order to evaluate a piecewise-defined function at a particular point, it is necessary to determine which of the function’s subdomains contains the point.

**Rules **

**Examples**

Find f(-3) and (0)

**Explanation**

As in the last example, it is important to be careful when reading the subdomain of each subfunction in the function. Both subdomains contain 0, but only the domain of x^{2} *includes* 0. This is usually a matter of taking note of whether the domain is expressed with <,> or ≤,≥.

The domain of a piecewise-defined function is a combination of its subfunctions’ individual subdomains.

**Examples**

**Explanation**

If there are one or more points in one or more subdomains at which the function is not defined, the function is said to be **discontinuous** at those points.

Graphing these functions is a matter of graphing each component subfunction on its subdomain.

**Examples**

**Explanation**

**Instructions**

Evaluate f(0)

Find f(-1)

Find f(0)- The absolute value function

is a piecewise-defined function. Express it in function notation.

Find the domain of h(x).

Find the domain of f(x).

Find the points at which g(x) is discontinuous.- Graph

- Graph

- Graph

- is undefined.

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