Answer:
IV Figure represent the given function f(x)=[tex]\mid x+2\mid[/tex]+1.
Step-by-step explanation:
Given function
f(x)=[tex]\mid x+2 \mid[/tex]+1
The given function can be write as
f(x)=(x+2)+1=x+3 when [tex]x\geq -2[/tex]
f(x)=-(x+2)+1 when [tex]x<-2[/tex]
f(x)=-x-1 when [tex]x<-2[/tex]
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 [tex]x\geq -2[/tex]
Therefore, f(x)= -2+3=1
Hence, IV figure is correct option.
