Answer:
Part 1) [tex]g(x)=-x^{2}[/tex]
Part 2) [tex]g(x)=(x+3)^{2}[/tex]
Part 3) [tex]g(x)=x^{2}+7[/tex]
Step-by-step explanation:
we have
The parent function is [tex]f(x)=x^{2}[/tex]
This is a vertical parabola open upward with vertex at origin (0,0)
Part 1) Reflection over the x-axis
The rule of the reflection across the x=axis is equal to
(x,y) ------> (x,-y)
so
f(x) -----> g(x)
The function g(x) will be
[tex]g(x)=-x^{2}[/tex]
Part 2) Horizontal shift left 3 units
The rule of the translation is
(x,y) ------> (x-3,-y)
so
f(x) -----> g(x)
The function g(x) will be
[tex]g(x)=(x+3)^{2}[/tex]
Part 3) Vertical shift up 7 units
The rule of the translation is
(x,y) ------> (x,y+7)
so
f(x) -----> g(x)
The function g(x) will be
[tex]g(x)=x^{2}+7[/tex]
Answer:
g(x) = -(x-4)².
Step-by-step explanation:
Given : parent function f(x) = x², Reflection over the x-axis , Horizontal shift left 3 units and Vertical shift up 7 units.
To find : define the function g(x) .
Solution : We have given
Parent function f(x) = x²
By the reflection rule over x axis : f(x) →→ - f(x).
So, f(x) = x² →→ - x².
By the translation rule : f(x) →→ →→ f(x+h-k).it mean function shifted horizontally to ward left. and vertically up by k units
Then it would be - x² →→ →→ - (x+3-7)².
f(x)→→ →→ g(x) = -(x-4)².
Therefore, g(x) = -(x-4)².
