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Calculus, 8th Edition,stewart; page 21 problem 41

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Evaluate f(-3), f(0), and f(2) for the piecewise defined function. Then sketch the graph of the function.

asked Jul 27, 2015 in CALCULUS by anonymous

1 Answer

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Step:1

The function is f(x)=\left\{\begin{matrix} x+2 & \textup{\textrm{if}} & x< 0 \\ 1-x & \textrm{if} &x\geq 0 \end{matrix}\right..

The function f(x) is called piecewise defined function.

Find the domain of f(x)=x+2.

If x<0 then the function is f(x)=x+2.

All possible values of x is the domain of the function.

The function does not have any radicals.

The domain of the function is the set of all real numbers.

Find the domain of f(x)=1-x.

If x\geq 0 then the function is f(x)=1-x.

All possible values of x is the domain of the function.

The function does not have any radicals.

The domain of the function is the set of all real numbers.

Domain of the piecewise function f(x)=\left\{\begin{matrix} x+2 & \textup{\textrm{if}} & x< 0 \\ 1-x & \textrm{if} &x\geq 0 \end{matrix}\right. is (-\infty , \infty ).

Step:2

Graph of the function f(x)=\left\{\begin{matrix} x+2 & \textup{\textrm{if}} & x< 0 \\ 1-x & \textrm{if} &x\geq 0 \end{matrix}\right..

Hallow circle indicates that the point is excluded from the function.

Solid circle indicates that the point is included in the function.

Solution:

Domain of the piecewise function f(x)=\left\{\begin{matrix} x+2 & \textup{\textrm{if}} & x< 0 \\ 1-x & \textrm{if} &x\geq 0 \end{matrix}\right. is (-\infty , \infty ).

Graph of the function f(x)=\left\{\begin{matrix} x+2 & \textup{\textrm{if}} & x< 0 \\ 1-x & \textrm{if} &x\geq 0 \end{matrix}\right. is

.

answered Jul 28, 2015 by dozey Mentor

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