Question

Consider the function f(x) = x^2 and the function g(x) shown below. How will the graph of g(x) differ from the graph of f(x)?

g(x) = f(x - 2) = (x - 2)^2

A. The graph of g(x) is the graph of f(x) shifted down 2 units.
B. The graph of g(x) is the graph of f(x) shifted to the right 2 units.
C. The graph of g(x) is the graph of f(x) shifted to the left 2 units.
D. The graph of g(x) is the graph of f(x) shifted up 2 units.

Answer 1

The graph of g(x) = f(x - 2) = (x - 2)^2 will be the graph of f(x) shifted to the right 2 units.

Step-by-step explanation:

The graph of g(x) = f(x - 2) = (x - 2)² will be the graph of f(x) shifted to the right 2 units.

When we substitute x - 2 into the function f(x) = x², it will shift the graph horizontally to the right by 2 units.

Therefore, the correct answer is B. The graph of g(x) is the graph of f(x) shifted to the right 2 units.