Question
The graph of a function f is shown in the figure above. At what value of x does f have a jump discontinuity?
A x=1
B x=3
C x=4
D x=5
Answer/Explanation
Ans:A
has a jump discontinuity at x=
Question
The function f has a removable discontinuity at x=
. Which of the following could be the graph of f?
A 
B 
C 
D 
Answer/Explanation
Ans:A
.This graph has a removable discontinuity at x=3, because \(\lim_{x\rightarrow 3^{-}}f(x)=\lim_{x\rightarrow 3^{+}}f(x)\) even though the function is not defined at x=3
Question
The function
is defined above. Which of the following statements is true?
A f is continuous at x=3.
B
has a removable discontinuity at
.
C f has a jump discontinuity at x=3.
D f
has a discontinuity due to a vertical asymptote at x=3.
Answer/Explanation
Ans:B
\(\lim_{x\rightarrow 3}=\lim_{x\rightarrow 3}\frac{2x^{2}-5x-3}{x-3}=\lim_{x\rightarrow 3}\frac{(x-3)(2x+1)}{(x-3)}=\lim_{x\rightarrow 3}(2x+1)=2.3+1=7\)
\(\lim_{x\rightarrow 3}f(x)=7\) but \(f(3)\neq 7\) so there is a removable discontinuity at x=3