Suppose h(x) = f (g(x)) and the graphs of f and g are shown below. Describe the continuity of h at x = 0.

Question

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

Answer 1

and the answer options are

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