Question

Which statement correctly describes the relationship between the graph of f(x)=x and the graph of g(x)=f(x+9) ?

A) The graph of g(x) is the graph of​​ f(x)​ vertically compressed by a factor of 9.
B) The graph of g(x) is the graph of​​​ f(x) translated 9 units right.
C)The graph of g(x) is the graph of f(x) translated 9 units left.
D) The graph of g(x) is the graph of​ f(x)​ vertically stretched by a factor of 9.

Answer 1

The correct relationship between the graph of f(x) = x and g(x) = f(x + 9) is that the graph of g(x) is translated 9 units to the left of the graph of f(x).

Step-by-step explanation:

The student has asked about the relationship between the graph of f(x) = x and the graph of g(x) = f(x + 9). The graph of f(x) is a straight line with a slope of 1, based on the equation provided. When we create the graph of g(x) by substituting x in f(x) with (x + 9), this shifts the original graph horizontally. Specifically, the graph of g(x) will be the graph of f(x) translated 9 units to the left. This is because every x-value on the graph of f(x) is replaced with an x-value that is 9 units greater in g(x), causing the entire graph to shift to the left by those 9 units.