Hard to tell which branch of the functions are defined at the discontinuity. That is, where is the solid dot, and where is the open circle?
g(0) is hard to figure, since "discontinuity at 0,1" doesn't give a clear picture. Also, you have (2,0) twice in the list of g's values.
Suppose h(x) = f (g(x)) and the graphs of f and g are shown below. Describe the continuity of h at x = 0.
how would you do this if you were given two graphs:
discontinuity at -2,0; point at -1,1; and point at 0,0 (to make a parabola)
then discontinuity at 0,-1; and then continuous points 1,-1; 2,-1, 3,-1....\
G- point at-2,-1; -1,0; discontinuity at 0,1
then point at 2,0; 1,1; 2,0; 3,1; 4,2
h is continuous at x = 0.
h is discontinuous at x = 0 since h(0) is undefined.
h is discontinuous at x = 0 since the limit of h(x) as x approaches 0 does not exist
h is discontinuous at x = 0 since the limit of h(x) as x approaches 0 does not equal 0
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