Question

Which functions are continuous at x= -2? Select all that apply.

Answer 1

(i) and (iii)

Explanation:

for i)

f(x) =
`(x^(2)-4)/(x+2)`

=
`((x+2)(x-2))/(x+2)`

=(x-2)

As x =-2

f(x)=-2-2

f(x)=-4

so it is a continuous function

for ii)

from the result of (i) we can deduce the result of second and we see that it is not equal to zero so it is not a continuous function

iii)

f(x)=
`(x^(2)+4x+4)/(x+2)`

f(x)=
`((x+2)^(2))/(x+2)`

f(x)=
`((x+2)(x+2))/(x+2)`

f(x)=x+2

as x= -2

f(x)=-2+2

f(x)=0

so it is a continuous function

iv) From the result of iii we can deduct that

f(x)=0 because it have the same equation so it is not a continuous function

Answer 2

The first and third functions are continuous at x=-2

Explanation:

Please, see the attached files.

Thanks.