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# At a Glance - Continuity at a Point via Formulas

It's good to have a feel for what continuity at a point looks like in pictures. However, sometimes we're asked about the continuity of a function for which we're given a formula, instead of a picture. When this happens, remember that the following three statements must all hold for f to be continuous at c.

1. I. The function f is defined at x = c.

2. The limit  exists.

3. The value f(c) agrees with the limit

#### Example 1

 Determine whether the function  is continuous at x = 1.

#### Example 2

 Determine whether the function   is continuous at x = 2.

#### Example 3

 Determine whether the function  is continuous at x = 0.

#### Example 4

 Determine whether the function is continuous at x = 0.

#### Example 5

 At what values is f discontinuous?

#### Exercise 1

Determine whether the function

is continuous at each given value. If not, explain.

• x = -5
• x = -4
• x = 0
• x = 2
• x = 3

#### Exercise 2

For what values of x is the function discontinuous.

#### Exercise 3

For the function, determine all values at which the function is discontinuous.

#### Exercise 4

For what values of x is h(x) discontinuous.