The problem asks to find the point $c$ at which the function has a jump discontinuity but is right-continuous.

Looking at the graph, the key characteristic of a jump discontinuity is a sudden "jump" in the value of the function. This means the function has a different value from the left and right at a certain point. Moreover, right-continuity means that the function approaches the same value from the right side.

Analysis:

• At $x = 2$, there is a jump. The function approaches $y = 3$ from the right side, but it has a different value (around $y = 1$) from the left. This indicates a jump discontinuity at $x = 2$, and the function is right-continuous here because as $x$ approaches 2 from the right, the value of the function approaches $y = 3$.

Thus, the point $c$ where the function has a jump discontinuity and is right-continuous is $c = 2$.

Do you have any further questions or need additional details?

Related Questions:

1. What is the difference between jump discontinuity and removable discontinuity?
2. How do you determine if a function is left-continuous at a point?
3. Can a function be both left-continuous and right-continuous but not continuous overall?
4. What are the common types of discontinuities in a function?
5. How does right-continuity impact the behavior of piecewise functions?

Tip: A jump discontinuity means that the limits from the left and right are different at a specific point, but the function can still be continuous from one side (right or left).