Consider the function f(x) = x²-5. If g(x) = f(x - 7), what can be said of g(x)? Check all that apply.
A The graph of g(x) is shifted seven units to the left of f(x).
B The graph of g(x) is shifted seven units to the right of f(x).
C The graph of g(x) is shifted seven units above f(x).
D The graph of g(x) is shifted seven units below f(x).
E The vertex of g(x) is (7,0).
F The axis of symmetry of g(x) is x = 7.
explain your answer
A. The graph of g(x) is shifted seven units to the right of f(x).
E. The vertex of g(x) is (7,0).
F. The axis of symmetry of g(x) is x = 7.
When we have g(x) = f(x - 7), this means that we are shifting the graph of f(x) to the right by 7 units. This is because the x value in f(x) is being replaced by x - 7 in g(x), causing a horizontal shift. The vertex of g(x) will be 7 units to the right of the vertex of f(x), so the vertex of g(x) will be (7,0). The axis of symmetry of g(x) will also be x = 7, as the vertical line passing through the vertex of g(x) will be at x = 7.