Question

Which graph represents the function f(x)=|x+2|+1

Answer 1

I believe the answer to this question is the one on the bottom right

Answer 2

IV Figure represent the given function f(x)=
`\mid x+2\mid`+1.

Explanation:

Given function

f(x)=
`\mid x+2 \mid`+1

The given function can be write as

f(x)=(x+2)+1=x+3 when
`x\geq -2`

f(x)=-(x+2)+1 when
`x<-2`

f(x)=-x-1 when
`x<-2`

Put x= 0 in the function

f(x)=x+3=0+3=3

Hence, the function intersect the y-axis at point (0,3).

Therefore, we can say I figure is false.Because in I figure the function intersect y-axis at point (0,-3).

The function break at x=-2 .

Hence, we can say II figure and III figure are false. Because in II figure the function break at x=2 and in III figure the function break at x=-1.

Put x=-2 in the given function

f(x)= x+3 when
`x\geq -2`

Therefore, f(x)= -2+3=1

Hence, IV figure is correct option.