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Continuity of Functions

Continuity of Functions

Continuity at a Point via Pictures Examples

Example 1

Look at the graph of the function f(x).

The following three statements must all hold for f to be continuous at c.

  • The function f is defined at x = c.
      
  • The limit  exists.
      
  • The value f(c) agrees with the limit .

For each given value of c, determine whether each of the three statements holds. Use this to determine whether f is continuous at the given value of c.

  • c = -2
      
  • c = -1
      
  • c = 0
      
  • c = 2
      
  • c = 5

Example 2

Look at the graph of the function f(x).

The following three statements must all hold for f to be continuous at c.

  • The function f is defined at x = c.
      
  • The limit  exists.
      
  • The value f(c) agrees with the limit .

For each given value of c, determine whether each of the three statements hold. Use this to determine whether f is continuous at the given value of c.

  • c = -2
      
  • c = -1
      
  • c = 0
      
  • c = 1
      
  • c = 2
      

Example 3

Look at the graph of the function f(x).

Determine whether the function f is continuous at each given value. If not, explain.

  • x = -2
      
  • x = 0
      
  • x = 2
      
  • x = 4
      
  • x = 5
      

Example 4

Look at the graph of the function g(x).

Determine whether the function g is continuous at each given value. If not, explain.

  • x = -20
      
  • x = -10
      
  • x = 0
      
  • x = 5
      
  • x = 10
      
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