A function is graphed on the coordinate plane.A rational function is graphed on the coordinate plane. It consists of two curves. The first curve starts on the left of the graph just below the x-axis. It decreases gradually until left-parenthesis 2 comma negative 3 right-parenthesis then quickly, approaching but never reaching x=3. The second curve starts at the top of the graph just to the right of x = 3 and decreases quickly until left-parenthesis 4 comma 3 right-parenthesis and then gradually approaching but never reaching the x-axis.

Question

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

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

The function has a removable discontinuity at x = 0.
The function has a removable discontinuity at x = 0.

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

The function has a nonremovable discontinuity at x = 0.
The function has a nonremovable discontinuity at x = 0.

Answer 1

The described function has a discontinuity at \( x = 3 \). The behavior of the function indicates that as \( x \) approaches 3 from the left, the function approaches negative infinity, and from the right of \( x = 3 \), the function starts at the top and decreases. Since there is a gap there (the left and right hand limits do not converge to the same value at that point), this situation represents a vertical asymptote rather than a removable discontinuity.

Therefore, the correct conclusion is:

The function has a nonremovable discontinuity at \( x = 3 \).