y = {-x, x < 2; x-4, 2 ≤ x < 3; 3x -10, 3 ≤ x < 5; x, 5 ≤ x}

Step-by-step explanation:

The absolute value function is a piecewise linear function that changes its definition when its argument changes sign.

Here, the three different absolute value expressions will change their behavior at three different values of x. That is, this equation will be described by a piecewise linear function in four (4) pieces.

For x < 2:

y = (3 -x) +(2 -x) -(5 -x) = -x

For 2 ≤ x < 3:

y = (3 -x) +(x -2) -(5 -x) = x -4

For 3 ≤ x < 5:

y = (x -3) +(x -2) -(5 -x) = 3x -10

For 5 ≤ x:

y = (x -3) +(x -2) -(x -5) = x

In summary, the equation can be written ...

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Additional comment

The absolute value function itself can be described by ...

Answer:y = {-x, x < 2; x-4, 2 ≤ x < 3; 3x -10, 3 ≤ x < 5; x, 5 ≤ x}

Step-by-step explanation:The

absolute valuefunction is apiecewise linearfunction that changes its definition when itsargument changes sign.Here, the three different absolute value expressions will change their behavior at three different values of x. That is, this equation will be described by a piecewise linear function in four (4) pieces.

For x < 2:

y = (3 -x) +(2 -x) -(5 -x) = -x

For 2 ≤ x < 3:

y = (3 -x) +(x -2) -(5 -x) = x -4

For 3 ≤ x < 5:

y = (x -3) +(x -2) -(5 -x) = 3x -10

For 5 ≤ x:

y = (x -3) +(x -2) -(x -5) = x

In summary, the equation can be written ...

_____

Additional commentThe absolute value function itself can be described by ...