Respuesta :

The piecewise function graphed below is given as follows:

  • [tex]f(x) = 3, -4 \leq x \leq -2[/tex]
  • [tex]f(x) = x + 2, -2 < x \leq 3[/tex]
  • [tex]f(x) = -1, 3 < x \leq 5[/tex]

What is a piecewise function?

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

For x between -4 and -2, inclusive, the function is constant at 3, hence the definition is:

[tex]f(x) = 3, -4 \leq x \leq -2[/tex]

For x greater than -2 until 3, the function is a line with slope 1 and y-intercept 2, hence the definiton is:

[tex]f(x) = x + 2, -2 < x \leq 3[/tex]

For x greater than 3 until 5, the function is constant at -1, hence the definition is:

[tex]f(x) = -1, 3 < x \leq 5[/tex]

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

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