I have two problems.. I'll put them both here, and show my work on both of them. 1. Is this function continuous on [-1, 1]? f(x) = x / |x| , x does not equal 0 0 , x = 0 After graphing this function, the first statement gives y = -1 for all x < 0, and y = 1 for all x > 0. The second statement makes y = 0 when x = 0. Putting everything together, y values are defined at -1, 0, 1, but nothing in-between. Does this make the function not continuous because of the jumping at x = 0? 2. Discuss the continuity of the function g: g(x) = sin x / x , for x does not equal 0 1/2 , for x = 0 There is a hole in the graph at x = 0 (for the first statement), but the second statement defines x = 0 to be 1/2, it's just lower than the curve in the first statement. Would this be a continuous function or not?