Use a graphing utility to graph the function.

Question

Explain why there is no vertical asymptote when a superficial examination of the function may indicate that there should be one.

(a) The graph is a vertical line

(b) The function does not have a discontinuity.    

(c) There is a jump discontinuity at (3, 2).

(d) The denominator is never equal to zero.

(e) There is a hole at (3, 2).

Answer 1

If you factor the numerator you find out there is a "3 - x" factor in it that cancels with the "3 - x" in the denominator:

This manifests itself as a hole in the graph at x = 3 (so (3, 2)) and not a vertical asymptote. So answer (e) is correct.