The task in this image is to determine the type of discontinuity for each graph. Below, I will provide a brief explanation for the types of discontinuities and identify them based on the provided images:

1. First graph:

   • The function has a jump discontinuity because the left-hand limit and the right-hand limit exist but are not equal.

2. Second graph:

   • The function has a removable discontinuity because there is a hole (missing value) in the graph, but the limits from both sides are equal.

3. Third graph:

   • The function has a cusp (or sometimes referred to as a non-differentiable point) because the slope abruptly changes, but there is no actual discontinuity in the function.

4. Fourth graph:

   • The function has an infinite discontinuity because the values diverge towards positive and negative infinity.

Let me know if you want detailed reasoning for any graph or any further help!

Related Questions:

1. What are the formal definitions of jump, removable, and infinite discontinuities?
2. How can we determine the type of discontinuity from a function equation?
3. What is the difference between a cusp and a point of discontinuity?
4. How do limits help in analyzing the behavior of discontinuities?
5. Can all discontinuities be "fixed" (e.g., removable discontinuities)?

Tip:

Always check the behavior of limits from both sides of a point to identify the type of discontinuity!