Where is this graph discontinuous? Which discontinuities are removable and which

Question

Where is this graph discontinuous?

Which discontinuities are removable and which are not?

Does the limit of this function exist as x approaches -2?Why or Why Not? If so, what is it?

Is this graph continuous at -2?Why or Why not?

If it is not continuous what exists in the graph at x = -2?

Does the limit of this graph exist as x approaches zero? Why or Why Not?

Is this graph continuous at 4? Why or Why not?

What is the limit of this function as x approaches 4 from the left?

How about the right? What exists in the graph at x = 4?

Does there appear to be a limit as x approaches positive infinity? If so, what is it?

What exists in the graph as x approaches infinity?

Using set notation describe where this graph is continuous.

Explanation / Answer

1. DISCONTINUOUS at: x= -2,4 2. removable at x= -2 and non removable at x=-4 3. limit exists at x=-2 since LHS limit= RHS limit and that is equal to 9 4. not continuous. since value of limit is not equal to the value of the function at that point. 5. at x=-2 value of function =-2 and its point discontinuity. 6. yes it exists as LHS limit= RHS limit = value of function at that point. 7. yes it exists and is equal to 0 8. no graph is not continuous as LHS limit = -infinity and RHS limit = infinity. 9. -infinity 10. infinity 11. yes at x= 4+ graph goes to +ve infinity 12. as x goes infinity graph goes towards 0 13. graph is continuous from (-infinity, -2), (-2,4), (4,infinity )

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.