explain how to graph the given piecewise-defined function. be sure to specify the type of endpoint each piece of the function will have and why.

A function that is defined by many sub-functions, each of which applies to a specific interval of the main function's domain, is known as a piecewise-defined function (also known as a piecewise function or even a hybrid function) (a sub-domain).

The stated function is-

-x + 3 ; x < 2

3 ; 2 ≤ x < 4

4 - 2x ; x ≥ 4

Due to x being bounded, the graph of f(x) = -x + 3 is drawn for x smaller than 2.
Because x is bounded (greater than or equal to 2, but less than 4), the graph of f(x) = 3 is drawn.
For x higher than or equal to 4, the graph of f(x) = 4 - 2x is drawn since x is bounded.

For greater clarity, see the graph that is attached.

Purple is the representation of f(x) = -x + 3.
Orange is a representation of f(x) = 3.
Green represents the equation f(x) = 4 - 2x.

To know more about the piecewise-defined function, here

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The complete question is-

Explain how to graph the given piecewise-defined function. Be sure to specify the type of endpoint each piece of the function will have and why. f(x) = StartLayout enlarged left-brace 1st Row 1st column negative x + 3, 2nd column x less-than 2 2nd row 1st column 3, 2nd column 2 less-than-or-equal-to x less-than 4 3rd Row 1st column 4 minus 2 x, 2nd column x greater-than-or-equal-to 4 EndLayout