Answer:
see the attached figures
Step-by-step explanation:
Part 1) we have
The vertex is the point [tex](1,0)[/tex]
The equation of the line of the left side is [tex]y=-x+1[/tex]
The equation of the line of the right side is [tex]y=x-1[/tex]
The range of the function is equal to [tex]y\geq 0[/tex]
therefore
The absolute function will be equal to
[tex]y=\left|x-1\right|[/tex]
see the attached figure N 1
Part 2) we have
The vertex is the point [tex](0,1)[/tex]
The equation of the line of the left side is [tex]y=x+1[/tex]
The equation of the line of the right side is [tex]y=-x+1[/tex]
The range of the function is equal to [tex]y\leq 1[/tex]
therefore
The absolute function will be equal to
[tex]y=-\left|x\right|+1[/tex]
see the attached figure N 2
Part 3) we have
The vertex is the point [tex](1,-1)[/tex]
The equation of the line of the left side is [tex]y=-x[/tex]
The equation of the line of the right side is [tex]y=x-2[/tex]
The range of the function is equal to [tex]y\geq -1[/tex]
therefore
The absolute function will be equal to
[tex]y=\left|x-1\right|-1[/tex]
see the attached figure N 3
Part 4) we have
The vertex is the point [tex](-1,0)[/tex]
The equation of the line of the left side is [tex]y=-x-1[/tex]
The equation of the line of the right side is [tex]y=x+1[/tex]
The range of the function is equal to [tex]y\geq 0[/tex]
therefore
The absolute function will be equal to
[tex]y=\left|x+1\right|[/tex]
see the attached figure N 4
Part 5) we have
The vertex is the point [tex](-1,1)[/tex]
The equation of the line of the left side is [tex]y=x+2[/tex]
The equation of the line of the right side is [tex]y=-x[/tex]
The range of the function is equal to [tex]y\leq 1[/tex]
therefore
The absolute function will be equal to
[tex]y=-\left|x+1\right|+1[/tex]
see the attached figure N 5
