Your graph clearly shows that this function is discontinuous at x = 0.grace77 said:
grace77 said:
A point of discontinuity is a point on a graph where the function is not defined or experiences a sudden jump in value. It is a break or interruption in the continuity of a function.
The point of discontinuity for y=|x|/x can be found by setting the denominator (x) equal to 0 and solving for x. In this case, x=0 is the point of discontinuity.
Since the absolute value function is defined as the positive value of the input, when x=0, the denominator becomes 0 and the function becomes undefined. Therefore, x=0 is the point of discontinuity for y=|x|/x.
No, the point of discontinuity cannot be removed as it is a fundamental characteristic of the function. However, the function can be modified to remove the point of discontinuity by defining it separately for x<0 and x>0.
The point of discontinuity for y=|x|/x at x=0 causes a break in the graph, resulting in two separate branches for x<0 and x>0. This creates a V-shaped graph with an open circle at the point of discontinuity.