Suppose f(x) is defined as shown below. Use the continuity checklist to show tha
ID: 2876229 • Letter: S
Question
Suppose f(x) is defined as shown below. Use the continuity checklist to show that f is not continuous at 3. Is f continuous from the left or right at 3? State the interval(s) of continuity. f(x) = {x^2 + 3x if x>3 3x if x lessthanorequalto 3 Why is f not continuous at 3? lim_x rightarrow f(x) does not exist. f(3) is not defined. Although lim_x rightarrow f(x) exists, it does not equal f(3). Choose the correct answer below. f is continuous from the left at 3. f is not continuous from the left or the right at 3 f is continuous from the right at 3 What are the interval(s) of continuity? (Type your answer in interval notation. Use a comma to separate answers as neededExplanation / Answer
A)
To the left of x=3, f(x) is x^2+3x and we know that polynomial is always continues.
To the right of x=3 , we have f(x) as 3x, which is again polynomial.
Now , f(x) is continues every where , it means left hand and right hand value should be same.
(3)^2+3(3) = 3(3) => 18 = 9 , Which is not equal , Hence f(x) is not continues at x=3. So choice A is correct.
B)
Choice A and C both are correct, we have already proved this inpart A.
C) (-infinity , 3) U [ 3,infinity )