Continuity question again ---please help?

Question

Hi,

Am asking this again, as i did not write out the question clear enough the first time.

if

f(x) = -5√(x+1) if x is greater than 0

8*x^3+1 if x is less than or equal to 0

the which of the following statements are correct

1. f is a cubic function

2. f is discontinuous at x = 0.

3. f is continuous at x = 0.

4. f is a square root function.

5. f is continuous at x = -1.

2 and 5 are correct are any more correct?

Thanks for any help received, it is very much appreciated.

Answer 1

you're right 2 and 5 are the only correct answers

1 is false because not all of f is a cubic

3 is false because there is a non-removable discontinuity (a jump) at x = 0. The limit from the left does not equal the limit from the right.

4 is false because not all of f is a square root function

ADD ON

the limit from the right as x approaches 0 is -5 unless you typed it in wrong. The limit is 1 from the left

Answer 2

2 and 5 are indeed true

1 is true for x =< 0, but not true elsewhere

3 cannot be true since 2 is true

4 is true fo x>0 but is untrue elsewhere

Answer 3

You are right :

answer 2 and 5 are correct

and there aren't any more

that are correct.