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)= 3, x + 3, X < 2 25 x < 4 4 – 2x, x 2 4​

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Answer:

Indicate on the x-axis the boundaries defined by the intervals on each piece of the domain.

For each piece of the domain, graph on that interval using the corresponding equation pertaining to that piece.

You would graph the equation f(x) = –x + 3 for input values less than 2. There would be an open circle at the point (2, 1) since the domain for the first piece does not include 2. You would then graph a horizontal line at f(x) = 3 for input values between 2 and 4. There would be a closed circle at (2, 3) and an open circle at (4, 3). Last, you would graph f(x) = 4 – 2x for input values greater than or equal to 4. There would be a closed circle at the point (4, –4) since 4 is in the domain of the third piece.

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