Help? Describe the domain and range of this piecewise function

Question

y= {2x, if x < -1

     {-2x, if x ≥ -1

Answer 1

A sketch will help.  Each of your pieces is a linear function (straight line), with the change happening at x=-1.  Since x=-1 is covered by the second function, your domain is all real numbers.  But a graph will show what is happening at x=-1.  On the left piece, the 2x graph, 2(-1)=-2.  Note this point is not on the graph, but this is where the left piece ends (-1,-2).  The right half starts at x=-1, and y=(-2)(-1)=2.  So your graph starts on the left with an 'uphill" line, but at x=-1, it suddenly jumps from that not included (-1,-2) point up to the first point on the second half, (-1,2).  There is a discontinuity here.  This is also the "high" point of the graph, which will limit the range to < 2.

 

Domain (-infinity, infinity) or all real numbers

Range, (-infinity, 2]