Math/Algebra
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Sketch the graph of each piecwisedefined function. Determine the domain and range. Identify each point of discontinuity.
f(x)= x if x<0
42x if 0 <or= x<3
2x+1 if x >= 3

With a soft pencil and a good eraser, draw the following lines
y = x , use (0,0) and (4,4) to sketch it
y = 4  2x , use (0,4) and (2,0) to sketch it
y = 2x + 1 , use (0,1) and (3,7) to sketch it
erase the overlapping lines, leaving only the parts in the given domains.
Make special note of the "transition" points, noting carefully if the point is included or excluded
e.g. for y = x, the point (0,0) would be excluded but the point (0,4) would be included in y = 42x
To include a point, the common way is to draw it as a solid point, to exclude it, draw it as an open point
(like a little o )