Continuity

On the interval [-7, 7] where is the function f not continuous?

• -2, 2

• 2

• -2

• nowhere

Tags

CCSS.HSF-IF.C.7D

Find the value of k, if possible, that makes the function f continuous everywhere.

• 3

• 0

• 2

• no such k exists

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Use the definition of continuity to determine whether the function is continuous at x = 7.

• Yes, it's continuous at x = 7.

• No, it's not continuous because the function is not defined at x = 7.

• No, it's not continuous because the limit does not exist as x approaches 7.

• No, it's not continuous because the value at x = 7 does not equal the limit.

Tags

CCSS.HSF-IF.C.7B

Find all values of k that would make the function f(x) continuous.

• 2

• 3

• 4

• 5

Tags

CCSS.HSF-IF.C.7B

The graph of y = f(x) is shown. Is the function continuous over the interval (-2, 3)? If not, why not?

• yes

• no, the limit does not exist at x = 0.5

• no, f(0.5) does not equal the limit of f(x) at x = 0.5

• no, the function is not defined at x = 0.5

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

Is the function shown below continuous on the interval [-5, 0]?

 $g\left(x\right)=\frac{2}{x+3}$  

• yes

• no, because g(0) does not exist

• no, because g(-3) does not exist

• no, because the value of g(-3) is not equal to the limit at x = -3

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.REI.D.11

What type of discontinuity occurs at x = 2 and what step of continuity is broken?

• jump and f(2) does not exist

• removable and f(2) does not exist

• jump and the limit as x approaches 2 does not exist

• infinite and the limit as x approaches 2 does not exist

Tags

CCSS.HSA.REI.D.10

Is the function continuous over the interval [-4, 4]? If not, why?

• yes

• no, the limit does exist at x = -1

• no, the limit does not exist at x = 4

• no, the function is not defined at x = -1

Tags

CCSS.HSF-IF.C.7D

Which of the following is correct about f at x = 3?

I: the limit as x approaches 3 exists

II: f is defined at x = 3

III: f is continuous at x =3

• II only

• I and II

• II and III

• I, II, and III

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

Over which interval is the function continuous?

• [-6, -1]

• [-1, 1]

• [1, 6]

• None of the Above

Tags

CCSS.HSF-IF.C.7D