Question

Which statement is true about the discontinuities of the function f(x)?

A) There are holes at x=7 and x=-4/3
B) There are asymptotes at x=7 and x=-4/3
C) There are asymptotes at x=-7 and x=4/3
D) There are holes at (-7,0) and x=4/3

Answer 1

The correct statement is that there are holes at x=7 and x=-4/3 in the function f(x).

Step-by-step explanation:

The correct statement about the discontinuities of the function f(x) is option A) There are holes at x=7 and x=-4/3.

A hole in a function occurs when a point is removed from the graph, leaving a hole that can be filled by assigning a new value to the function at that point. In this case, the function has a hole at x=7 and x=-4/3.

Option B) There are asymptotes at x=7 and x=-4/3 is incorrect. Asymptotes are lines that the graph approaches but does not touch, and they do not correspond to the given function.

Options C) There are asymptotes at x=-7 and x=4/3 and D) There are holes at (-7,0) and x=4/3 are also incorrect as they do not correspond to the given function.