Math Question
![\[
f(x)=|x+2|, \quad-4<x<-1
\]
Sketch the graph of the function \( f(x) \). Choose the correct graph below.
A.
B.
C.
0.
Determine whether the function has any absoluse extreme values on iss domain. Choose the correct answer below.
A. The function has an absolute minimum value at \( x=-2 \) but does not have an absolute maximum value on is domain.
8. The function has an absolute maximum value at \( x=-4 \) and an absolute minimum value at \( x=-2 \) on its domain.
c. The fundion has an absolute maimum value at \( x=-4 \) but does not have an absolute minimum value on its domain.
D. The function does not have any absolute extreme values on its domain.
Explain the results in terms of the extreme value theorem.
A. Since the function \( f \) is continuous on a closed interval, \( f \) attains both an absolute maximum value and an absclute minimum value on its domain.
B. Since the function \( f \) is not continuous on a closed interval, \( f \) may or may not have any absolute extreme values on its domain.
C. Since the function \( f \) is continuous on an open interval, \( f \) may or may not have any absolute extreme values on its domain.
D. Since the function \( f \) is not continuous on an open interval, \( f \) does not attain any absolute extreme values on its domain.](https://d3hlidq5bf9vg0.cloudfront.net/app-server-student/2022/4/16/a19e31eb-0daa-4ded-8d88-e46831b4bb10.png "\[
f(x)=|x+2|, \quad-4<x<-1
\]
Sketch the graph of the function \( f(x) \). Choose the correct graph below.
A.
B.
C.
0.
Determine whether the function has any absoluse extreme values on iss domain. Choose the correct answer below.
A. The function has an absolute minimum value at \( x=-2 \) but does not have an absolute maximum value on is domain.
8. The function has an absolute maximum value at \( x=-4 \) and an absolute minimum value at \( x=-2 \) on its domain.
c. The fundion has an absolute maimum value at \( x=-4 \) but does not have an absolute minimum value on its domain.
D. The function does not have any absolute extreme values on its domain.
Explain the results in terms of the extreme value theorem.
A. Since the function \( f \) is continuous on a closed interval, \( f \) attains both an absolute maximum value and an absclute minimum value on its domain.
B. Since the function \( f \) is not continuous on a closed interval, \( f \) may or may not have any absolute extreme values on its domain.
C. Since the function \( f \) is continuous on an open interval, \( f \) may or may not have any absolute extreme values on its domain.
D. Since the function \( f \) is not continuous on an open interval, \( f \) does not attain any absolute extreme values on its domain.")
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