the function f is defined as follows `f(x)=x+3` if `-2<=x<1` , `f(1)=9` , `f(x)=-x+2` if `x>1` . find domain range and graph must show work

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This function is has three parts to it.  When `-2<=x<1` , it is the straight line `x+3` , when `x=1` , it is the single value 9, and when `x>1` , it is the straight line `-x+2` .

The domain of the function is all x-values that are greater than...

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This function is has three parts to it.  When `-2<=x<1` , it is the straight line `x+3` , when `x=1` , it is the single value 9, and when `x>1` , it is the straight line `-x+2` .

The domain of the function is all x-values that are greater than or equal to -2.  

The range is a little more work.  Consider the region `-2<=x<1` first.  The y-values are from `f(-2)=-2+3=1` to `1+3=4` in a straight line.

The region at x=1 has y-value 9.

The last region is from x>1 and the one endpoint is `-1+2=1` to negative infinity.

This means the range is `{y in R|y=9, y<4}` and the domain is `x>=-2` `` .

To graph the function, we need to graph the lines in each section along with the dot at (1,9).  This is the graph:

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