Which statement correctly describes the relationship between the graph of f(x) and g(x)=f(x−7) ? a) the graph of g(x) is the graph of f(x) translated 7 units down. b) the graph of g(x) is the graph of f(x) translated 7 units left. c) the graph of g(x) is the graph of f(x) translated 7 units right. d) the graph of g(x) is the graph of f(x) translated 7 units up.

Assume that f(5)=8. So, (5, 8) is a point in the graph of f.

For g(x) to give us 8, we need x to be 12, because in that case we would have:

      g(12)=f(12-7)=f(5), which is 8. Thus, (12, 8) is a point on the graph of g.

Comparing (5, 8) in f, and (12, 8) in g, we can see that the graph of g is the graph of f shifted 7 units to the right.

 C) The graph of g(x) is the graph of f(x) translated 7 units right.