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Continuity of Functions

Continuity of Functions

Continuity of Functions: A Hop, Skip, and a Jump Quiz

Think you’ve got your head wrapped around Continuity of Functions? Put your knowledge to the test. Good luck — the Stickman is counting on you!
Q.
  • Consider the following statements:

I. f(c) is defined

II.  exists

III. 

We say "f is continuous at c" if which of the following statements hold?



I
II
I, II
I, II, III
Q. Which of the statements is true about the function f graphed below? 



f is discontinuous at x = 1 because f(1) does not exist.

f is discontinuous at x = 1 because  does not exist.

f is discontinuous at x = 1 because 
f is continuous at x = 1.

Q. Let  

Identify all points at which f is discontinuous.



x = 0, x = 1

x = 1, x = 2

x = 0, x = 2

x = 0, x = 1, x = 2

Q. Identify all points at which f is discontinuous. 



x = 1, x = -2
x = 1, x = 3
x = -2, x = 3
x = 1, x = -2, x = 3

Q. On which of the following intervals is f continuous? 

 



(-1, 1)
(0, 3)
(2, 4)
(0, 4)
Q. On which of the following intervals is f discontinuous? 

 



(-10, 2)
(2, 4)
(3, 4)
(3, 5)
Q. Let     

On which of the following intervals is f continuous?



(-2, 0)
(1, 5)
(4, 6)
(-1, 1)
Q. Let  

On which of the following intervals is f(x) continuous?



(-1, 1)
[0, 1)
(-1, 0]
[-1, 1]
Q. Let f(x) = x + 1 and g(x) = x – 1. Which of the following statements is false?



The function  is continuous at x = 1.

The function  is continuous at x = -1.

The function f + g is continuous at x = 1.

The function  is continuous at x = 1.

Q. Which of the following functions is not continuous?


f(x) = ex

g(x) = sin(x)

h(x) = tan(x)

m(x) = x2 – 2x + 3

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