Answer :

The graph of the given piecewise function is given at the end of the answer.

What is a piecewise function?

A piecewise function is a function that has different definitions, depending on the input.

For this problem, the function is defined as follows:

  • f(x) = 2/3x, for x ≤ 0.
  • f(x) = 3, for 1 ≤ x ≤ 3.
  • f(x) = -2x + 5, for x ≥ 4.

Hence:

  • To the left of x = 0, the function is increasing and linear.
  • Between x = 1 and x = 3, the function is constant at x = 3.
  • To the right of x = 4, the function is decreasing and linear.

The function is given at the graph with the end of answer, with holes where the function is not defined, and multiple behaviors as it is piecewise.

More can be learned about piecewise functions at https://brainly.com/question/27262465

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