# 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