Answer:
Part 1) ---> Translated up by 1 units
Part 2) ---> Reflected across the x-axis
Part 3) ---> Translated left by 1 unit
Part 4) ----> Translated right by 1 unit
Part 5) ----> Reflected across the y-axis
Part 6) ----> Translated down by 1 unit
Step-by-step explanation:
we know that
The parent function is
----> this is a vertical parabola open downward with vertex at (0,-1)
<em>Calculate each case</em>
Part 1) Translated up by 1 unit
The rule of the translation is
(x,y) -----> (x,y+1)
so
(0,-1) ----> (0,-1+1)
(0,1) ----> (0,0) ----> the new vertex
The new function is equal to
Part 2) Reflected across the x-axis
The rule of the reflection is
(x,y) -----> (x,-y)
so
(0,-1) ----> (0,1) ----> the new vertex
The new function is equal to
Part 3) Translated left by 1 unit
The rule of the translation is
(x,y) -----> (x-1,y)
so
(0,-1) ----> (0-1,-1)
(0,1) ----> (-1,-1) ----> the new vertex
The new function is equal to
Part 4) Translated right by 1 unit
The rule of the translation is
(x,y) -----> (x+1,y)
so
(0,-1) ----> (0+1,-1)
(0,1) ----> (1,-1) ----> the new vertex
The new function is equal to
Part 5) Reflected across the y-axis
The rule of the reflection is
(x,y) -----> (-x,y)
so
(0,-1) ----> (0,-1) ----> the new vertex
The new function is equal to
Part 6) Translated down by 1 unit
The rule of the translation is
(x,y) -----> (x,y-1)
so
(0,-1) ----> (0,-1-1)
(0,1) ----> (0,-2) ----> the new vertex
The new function is equal to
