Determine all discontinuities that exist on the graph of y = f(x) shown below. Please show your reasoning by justifying your answer with the conditions of continuity. If there is a discontinuity, identify it as removable or non-removable.
Where is graph y = f(x) ?
To determine the discontinuities on the graph of y = f(x), we need to analyze the conditions of continuity. A function is continuous if three conditions are met:
1. The function is defined at that point.
2. The limit of the function exists at that point.
3. The limit of the function at that point is equal to the value of the function at that point.
Let's analyze the possible types of discontinuities:
1. Removable Discontinuity: A removable discontinuity occurs when there is a hole or a gap in the graph at a certain point, but the limits approaching that point from both sides exist and are equal. This means that we can redefine the function at that point to make it continuous.
2. Non-removable Discontinuity: A non-removable discontinuity occurs when there is a jump, vertical asymptote, or a vertical line on the graph at a certain point. It happens when the limit of the function as it approaches from one side is not equal to the limit from the other side.
To identify these discontinuities, we need to look for the presence of holes, vertical asymptotes, jumps, or vertical lines on the graph.
Please provide the graph of y = f(x) for further analysis.