Question

Which statement correctly describes the relationship between the graph of f(x)=x and the graph of g(x)=f(x+3)?

A.) The graph of g(x) is the graph of f(x) translated 3 units right.
B.) The graph of g(x) is the graph of f(x) vertically stretched by a factor of 3.
C.) The graph of g(x) is the graph of f(x) translated 3 units left.
D.) The graph of g(x) is the graph of f(x) vertically compressed by a factor of 3.

Answer 1

The graph of g(x) = f(x + 3) is the graph of f(x) translated 3 units right.

Step-by-step explanation:

The correct statement that describes the relationship between the graph of f(x) = x and the graph of g(x) = f(x + 3) is A.) The graph of g(x) is the graph of f(x) translated 3 units right.

To see why, let's examine the effect of the transformation f(x + 3) has on the graph of f(x) = x. When we replace x in the function with (x + 3), we are shifting the graph 3 units to the left. Therefore, the graph of g(x) = f(x + 3) is the graph of f(x) translated 3 units to the right.