A function is graphed on the coordinate plane. It is a parabola with an open circle at the vertex left-parenthesis 3 comma 0 right-parenthesis. There is a point graphed at left-parenthesis 3 comma 3 right-parenthesis that is not on the parabola.

Question

Question
Use the graph to answer the question.
Describe the continuity of the graphed function.
(1 point)
Responses

The function is continuous.
The function is continuous.

The function has a removable discontinuity at x = 3.
The function has a removable discontinuity at x = 3.

The function has a jump discontinuity at x = 3.
The function has a jump discontinuity at x = 3.

The function has an infinite discontinuity at x = 3.
The function has an infinite discontinuity at x = 3.

Answer 1

The correct response is:

The function has a removable discontinuity at x = 3.

This is because the vertex of the parabola is at (3, 0) but is represented by an open circle, indicating that the function does not take on that value at x = 3. However, since the function approaches a limit at that point (the value of the parabola close to x = 3), it indicates a removable discontinuity. The point (3, 3) does not belong to the function, reinforcing this conclusion.