Question

Explain why the function is discontinuous at the given number a . Sketch the graph of the function.

f (x) = 1/(x + 2)                            a = - 2

Answer 1

Step 1:

The function is , .

 A function is continuous at , if then it should satisfy three conditions :

(1) is defined.

(2) exists.

(3) .

Substitute in above expression.

is undefined at .

does not satisfies the condition.

So is discontinuous at .

Graph :

As approaches to -2 from left hand side, tends to .

As approaches to -2 from right hand side, tends to .

The function does not exist because the left and right limits are different.

The function is discontinuous at .

Solution :

The function is discontinuous at .