T/F: If a function has a vertical asymptote at x = 2, then f(2) is undefined.

Question

 

 

ANSWER: False

#31, practice problems

Answer 1

Vertical asymptotes are x values where a function f(x) is undefined.  Since the vertical asymptote is x=2.  f(x) is undefined at x=2.

 

However, x=2 can be a solution of f(x).  x=2 can be an x-intercept.  This means that the factor (x - 2) is in both the numerator and denominator of a rational function f(x).  When this happens, x=2 is a hole.

 

The part that x=2 can be a hole makes the statement about f(2) undefined false.