The graph is a piecewise defined function.

Observe the graph.

A straight line exists in the interval $\"0\\leq$ .

The end points of the straight line are $\"(0,$ and $\"(3,$ .

Standard form of line equation using the points $\"(x_{1},$ and $\"(x_{2},$ is $\"(y-$ .

Substitute $\"(x_{1},$ and $\"(x_{2},$ in the line equation.

$\"(y-$

$\"y-3=\\frac{-3}{3}(x)\"$

$\"y-3=-1(x)\"$

$\"y=-x+3\"$

The equation of the line is $\"f(x)=-x+3\"$ in the interval $\"0\\leq$ .

Observe the graph.

A straight line exists in the interval $\"3\\leq$ .

The end points of the straight line are $\"(3,$ and $\"(5,$ .

Standard form of line equation using the points $\"(x_{1},$ and $\"(x_{2},$ is $\"(y-$ .

Substitute $\"(x_{1},$ and $\"(x_{2},$ in the line equation.

$\"(y-$

$\"y=\\frac{4}{2}(x-3)\"$

$\"y=2(x-3)\"$

$\"y=2x-6\"$

The equation of the line is $\"f(x)=2x-6\"$ in the interval $\"3\\leq$ .

Then the piecewise function is $\"f(x)=\\left\\{\\begin{matrix}$ .

The function is $\"f(x)=\\left\\{\\begin{matrix}$ .