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

f(x) = x^2
g(x) = (x+3)^2-7
A) the graph of g is the graph of f translated to the right 3 units and up 7 units
B) the graph of g is the graph of f translated to the left 3 units and down 7 units
C) the graph of g is the graph of f translated up 3 units and to the left 7 units
D) the graph of g is the graph of f translated down 3 units and to the right 7 units

(x+3) means it has been shifted to the left

-7 means it has been shifted down
so, I guess B is the answer you want.

recall that (y-k) = f(x-h) means f(x) has been shifted in the positive directions by h and k.

The correct answer is A) the graph of g is the graph of f translated to the right 3 units and up 7 units.

Explanation:

To determine the transformations that change the graph of f(x) to the graph of g(x), we can compare the standard form of the two functions.

The standard form of f(x) = x^2 represents a parabola with its vertex at the origin (0, 0).

The standard form of g(x) = (x+3)^2-7 represents a parabola as well, but it has been translated to the right 3 units (the -3 inside the function) and up 7 units (the -7 outside the function).

Therefore, the correct transformation is that the graph of g(x) is the graph of f(x) translated to the right 3 units and up 7 units, which aligns with option A.

To determine the transformations that change the graph of f(x) = x^2 to the graph of g(x) = (x+3)^2-7, we need to compare the two equations.

The transformation (x+3) in g(x) represents a horizontal shift to the left by 3 units.
The transformation -7 in g(x) represents a vertical shift down by 7 units.

Therefore, the correct answer is B) the graph of g is the graph of f translated to the left 3 units and down 7 units.