Limits of Composite Functions

Which of the following is true?

• 
• 
• 
• 

Tags

CCSS.HSA.REI.C.6

CCSS.HSA.REI.C.7

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

Find  $g\left(f\left(2\right)\right)$  

• -4

• -2

• 0

• 4

Tags

CCSS.HSF-BF.A.1C

Find  $f\left(g\left(4\right)\right)$  

• 1

• -2

• -3

• -4

Tags

CCSS.HSF-BF.A.1C

• 0

• 1

• 2

• 3

• DNE

Answer explanation

Because the limit as x approaches 2 of g(x) does not exist (the left approaches -inf while the right approaches +inf) then the composite function cannot exist.

Tags

CCSS.HSF-BF.A.1C

• 0

• -1

• 1

• 3

• DNE

Answer explanation

Since g(x) is not continuous at x= -1 we cannot make a formal conclusion about the value of the limit.

Tags

CCSS.HSF-BF.A.1C

• 4

• -3

• -12

• 2

• DNE

Answer explanation

Since the limit of the inside function DNE then the composite function DNE

Tags

CCSS.HSF-BF.A.1B

• 0

• -1

• 1

• 3

• DNE

Tags

CCSS.HSF-BF.A.1C

• 0

• -1

• 2

• DNE

Answer explanation

Remember that the limit is the value that the function is approaching, so the limit of h(x) as x approaches 0 is zero. and f(0) = -1

Tags

CCSS.HSF-IF.C.7B

• 1

• 2

• -3

• 0

• DNE

Answer explanation

Tags

CCSS.HSF-BF.A.1B

• 1

• 2

• 3

• DNE

Answer explanation

Tags

CCSS.HSF-BF.A.1B