Continuity

State whether the function graphed is continuous on ​[−1,7​]. If​ not, where does it fail to be continuous and​ why?

• The graph is not continuous at x = 1, because the limit exists but the function is not defined at that point.

• The graph is not continuous at x = 1, because the values of the​ left-hand limit and the​ right-hand limit are not the same.

• 
  The graph is continuous on

  ​[−1​,7​].

Use the function and the accompanying figure to answer the following question.

Is f continuous at x =​ 2?

• YES

• NO

• YES

• NO

• The function is discontinuous at x = -2 and x = 2.

• The function is discontinuous at x = 0.

• The function is continuous for all x.

Which of the following best describes the continuity at x = 3?

• 
  

  Jump Discontinuity

  
  

• Removable Point Discontinuity

  
  

• Infinite Discontinuity

  
  

• Continous

• The function is continuous at the set of​ x-values (−∞, 3) ∪ (3, 10) ∪ (10, ∞).

  
  

• The function is continuous at the set of​ x-values (−∞, 5) ∪ (5 10) ∪ (10, ∞).

• The function is continuous at the set of​ x-values (−∞, 3/2) ∪ (3/2, 10) ∪ (10, ∞).

• YES

• NO

Which is NOT continuous?

• 
• 
• 
• 

• A hole occurs where x=3

• vertical asymptote at x=3

• vertical asymptote at x=5

• A hole occurs where x=5

• continuous

• discontinuous