Question

What transformations change the graph of (f)x to the graph of g(x)?

f(x) = x² ; g(x) = (x + 7)² + 9

The graph of g(x) is the graph of f(x) translated to the down 7 units and right 9 units.
The graph of g(x) is the graph of f(x) translated to the up 7 units and left 9 units.
The graph of g(x) is the graph of f(x) translated to the right 7 units and down 9 units.
The graph of g(x) is the graph of f(x) translated to the left 7 units and up 9 units.

Answer 1

the parent function is x^2, it seems that x^2 is becoming (x+7)^2, this transformation is like

F(x)=x^2 => F(X+7)=(x+7)^2

the result of this is shifting the graphs origin 7 units left

The addition of 9 is an addition outside the parent function which shifts it up or down.

therefore g(x) is a linear transform of 7 units left and 9 units up