The image you provided depicts a function graph that appears to be a rational or piecewise function, and it includes potential discontinuities. Discontinuities typically occur where:

• The function is undefined (division by zero or other undefined behavior).
• There is a jump (sudden change in function value).
• There is an infinite discontinuity (asymptote).

By examining the graph, we can infer discontinuous points:

1. At x = -2, the graph shows an open circle, which suggests a removable discontinuity. This means the function is not defined at this point but may be defined nearby.
2. At x = 2, another open circle exists, indicating another removable discontinuity.
3. There also appears to be a vertical asymptote at x = 0, which suggests an infinite discontinuity. The function approaches infinity as $x$ approaches 0 from both directions.

Discontinuous Points:

• x = -2 (removable discontinuity)
• x = 2 (removable discontinuity)
• x = 0 (infinite discontinuity)

Would you like further details on different types of discontinuities or more information about this graph?

Here are five questions that can expand your understanding:

1. What is the difference between a removable and a non-removable discontinuity?
2. How do we algebraically identify discontinuities in rational functions?
3. Can you explain why a vertical asymptote causes an infinite discontinuity?
4. How can piecewise functions result in jump discontinuities?
5. What are other common types of discontinuities in graphs of functions?

Tip: To determine whether a discontinuity is removable or non-removable, check if you can redefine the function at the discontinuous point to make it continuous.