Piecewise+Functions

Sample One

 * f is a function defined by

f( x ) = -1 if x <= -2

= 2 if x > -2

How to do it-

Find the domain and range of function f and graph it.

For f(x)=-1 you just graph a straight line on the y axis at -1. You do the same for f(x)=2. You then have an closed circle on the line at 2 at -2 because x>-2, and you erase everything less than -2. You have an open circle on the line at -1 at -2 because x<=-2, and you erase everything greater than -2. Graph-  **

Sample 2

 * f is a function defined by

f( x ) = x 2 + 1 if x < 2**

=**- x + 3 if x >**= 2 Find the domain and range of function f and graph it.

How to do it- x squared plus one means that the graph is a parabola and it moves up one on the y axis. There is an open circle at the 2 because the problem says x<2, so the parabola line stops at 2 and doesn't go any farther. also, when you graph -x plus three it is a line that has a negative slope of -1 that goes through the 2 on the y axis. Because x>=2, there is a closed circle and the line that is less than two is erased. 
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