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The graph is a piecewise defined function.

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In left hand side of the graph, a straight line exists from $\"\"$ .

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The end points of the straight line are $\"\"$ and $\"\"$ .

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Using two points form of a line equation is $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in the line equation.

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$\"\"$

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The equation of the line is $\"\"$ .

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In middle part of the graph, it is look like a half circle with radius 2 units in the interval $\"\"$ .

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Centre is located at origin.

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The standard form of a circle equation is $\"\"$ .

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$\"\"$

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Write the equation in terms of $\"\"$ .

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$\"\"$

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The graph shows the positive half circle, then the equation of the circle is $\"\"$ .

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In right hand side of the graph, a straight line exists from $\"\"$ .

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The end points of the straight line are $\"\"$ and $\"\"$ .

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Using two points form of a line equation is $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in the line equation.

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$\"\"$

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The equation of the line is $\"\"$ .

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Then the piecewise function is $\"\"$ .

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$\"\"$ .