Yes the graph of the function represents a linear piecewise function of x.
From the graph we can see that the function can be broken down into 3 distinct parts.
Let us take the first part of the graph which represents the function:
For values of x ranging from negative infinity to 0, the value of y is 2 .
So the function is of the form y = 2.
Now for the second slanting part of the function.
The function passes through the points (0,2) and (2,-2)
Slope of the line = (-2-2)/(2-0) = -2
Equation of the line :
y-2 = -2(x)
or, y + 2x = 2.
Now for the third part of the function is y = -2 for all x>2
Hence the piecewise function can be represented as for the domain of x:
{2 , x < -2 }
y = {2-2x , -2 ≤ x ≤ 2}
{-2 , x > 2}
Hence all parts are linear so the function is linear in nature.
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