Consider the function f(x)=x^2-5.If g(x)=f(x-7), what can be said of g(x)? Check all that apply.

Question

The graph of g(x) is shifted seven units to the left of f(x)

The graph of g(x) is shifted seven units to the right of f(x)

The graph of g(x) is shifted seven units above f(x)

The graph of g(x) is shifted seven units above f(x)

The vertex of g(x) is (7,0)

The axis of symmetry of g(x) is x=7.

Answer 1

g(x) = f(x-7) = (x-7)^2 - 5  

 

f(x) is a parabola with vertex at (0,-5) and axis of symmetry x = 0

g(x) is a parabola with vertex at (7,-5) and axis of symmetry x = 7  

 

g(x) is shifted seven units to the right of f(x).  g(x) is not shifted above or below f(x).