Hello, iluvmathbutitshard!

So I understand how to find where a discontinuity is,

but I am not sure how to remove it. Any tips?

(1) Identify and remove the discontinuities of: .

(a) discontinuity at , remove by making

(b) discontinuity at , cannot removed

(c) discontinuity at , remove by making

(d) discontinuity at , remove by making

When , we have: .

The function is discontinuous at

Note: .

The graph is the curve: with a "hole" at (-1, 1).

We find that: .

If we let , we can "plug the hole".

The answer is(a).

(2) Identify and remove the discontinuities of: .

(a) discontinuity at , remove by making

(b) discontinuity at , cannot removed

(c) discontinuity at , remove by making

(d) discontinuity at , remove by making

The function is: .

When , we have

The function is discontinuous at

Note: .

The graph is the curve: with a "hole" at (3, 11).

We find that: .

If we let , we can "plug the hole".

The answer is(c).