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Continuity of Functions

Continuity of Functions

Continuity of Functions: A Hop, Skip, and a Jump True or False

1.
  • 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

2. Which of the statements is true about the function f graphed below? 

-> f is discontinuous at x = 1 because 

3. Let  

Identify all points at which f is discontinuous. -> x = 1, x = 2


4. Identify all points at which f is discontinuous. 

-> x = 1, x = -2

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

  -> (0, 3)

6. On which of the following intervals is f discontinuous? 

  -> (3, 4)

7. Let     

On which of the following intervals is f continuous?

-> (-2, 0)

8. Let  

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

-> (-1, 1)

9. Let f(x) = x + 1 and g(x) = x – 1. Which of the following statements is false?

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


10. Which of the following functions is not continuous? -> h(x) = tan(x)



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