Answer:
The answer in the attached figure
Step-by-step explanation:
we have the parent function
[tex]y=-x^{2}-1[/tex]
case 1) Reflected across the x-axis
we know that
The rule of the transformation is
(x,y)------> (x,-y)
so
[tex]y=-(-x^{2}-1)[/tex]
[tex]y=x^{2}+1[/tex]
case 2) Reflected across the y-axis
we know that
The rule of the transformation is
(x,y)------> (-x,y)
so
[tex]y=-(-x)^{2}-1[/tex]
[tex]y=-x^{2}-1[/tex]
case 3) Translated left by 1 unit
we know that
The rule of the transformation is
(x,y)------> (x-1,y)
so
[tex]y=-(x+1)^{2}-1[/tex]
case 4) Translated right by 1 unit
we know that
The rule of the transformation is
(x,y)------> (x+1,y)
so
[tex]y=-(x-1)^{2}-1[/tex]
case 5) Translated down by 1 unit
we know that
The rule of the transformation is
(x,y)------> (x,y-1)
so
[tex]y=-(x)^{2}-1-1[/tex]
[tex]y=-(x)^{2}-2[/tex]
case 6) Translated up by 1 unit
we know that
The rule of the transformation is
(x,y)------> (x,y+1)
so
[tex]y=-(x)^{2}-1+1[/tex]
[tex]y=-(x)^{2}[/tex]
