## Continuity – (Part Two).

**Definition:**

(i) A function is said to be __continuous from the right__ at **a** if

We can see that, as the function approaches a certain **x**-value from the right, is defined and

And as the function approaches a certain **x**-value from the left, is not defined, i.e;

.

Therefore, we say that the function is continuous from the right at this point, but is discontinuous from the left.

(ii) A function is said to be __continuous from the left__ at **a** if

Here, it is clear from the graph that the function is continuous from the left as **x **approaches **3**. This is because the function is defined at **x = 3 **and,

However, from the right,

So, we can say that the function is continuous from the left, but discontinuous from the right, at the point **x = 3**.

We may also have a function where it is neither continuous at a point from the left or from the right but is defined elsewhere.…