Question

Suppose that (g(x) = f(x - 5)). Which statement best compares the graph of (g(x)) with the graph of (f(x))?

a. The graph of (g(x)) is shifted 5 units to the right compared to (f(x)).
b. The graph of (g(x)) is shifted 5 units to the left compared to (f(x)).
c. The graphs of (g(x)) and (f(x)) overlap completely.
d. The graphs of (g(x)) and (f(x)) have different shapes but the same vertex.

Answer 1

The graph of g(x) is shifted 5 units to the right compared to f(x).

Step-by-step explanation:

The graph of g(x) is shifted 5 units to the right compared to f(x).

To understand this, let's consider an example:

If the graph of f(x) is a straight line passing through the point (0, 2) and (3, 2), then the graph of g(x) will be the same straight line, but shifted 5 units to the right. So, the points on the graph of g(x) will be (5, 2) and (8, 2).