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Step-by-step Answer
PAGE: 22SET: ExercisesPROBLEM: 55
Please look in your text book for this problem Statement

The graph is a piecewise defined function.

Observe the graph.

A straight line exists in the interval 0\leq x\leq 3.

The end points of the straight line are (0, 3) and (3, 0).

Standard form of line equation using the points (x_{1}, y_{1}) and (x_{2}, y_{2}) is (y- y_{1})=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}(x-x_{1}).

Substitute (x_{1}, y_{1})=(0, 3) and (x_{2}, y_{2})=(3, 0) in the line equation.

(y- 3)=\frac{0-3}{3-0}(x-0)

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 x\leq 3.

Observe the graph.

A straight line exists in the interval 3\leq x\leq 5.

The end points of the straight line are (3, 0) and (5, 4).

Standard form of line equation using the points (x_{1}, y_{1}) and (x_{2}, y_{2}) is (y- y_{1})=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}(x-x_{1}).

Substitute (x_{1}, y_{1})=(3, 0) and (x_{2}, y_{2})=(5, 4) in the line equation.

(y- 0)=\frac{4-0}{5-3}(x-3)

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 x\leq 5.

Then the piecewise function is f(x)=\left\{\begin{matrix} -x+3 & \textrm{if} & 0\leq x\leq 3\\ 2x-6 & \textrm{if} & 3<x\leq 5 \end{matrix}\right..

The function is f(x)=\left\{\begin{matrix} -x+3 & \textrm{if} & 0\leq x\leq 3\\ 2x-6 & \textrm{if} & 3<x\leq 5 \end{matrix}\right..



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