If g(x) respresents a quadratic function, which of the following best describes the relationship between the graphs of `g(x) and g(x-3)`?

Options

A. The graph of g(x-3) is 3 units to the left of the graph of g(x).
B. The graph of g(x-3) is 3 units to the right of the graph of g(x).
C. The graph of g(x-3) is 3 units lower than the graph of g(x).
D. The graph of g(x-3) is 3 units higher than the graph of g(x).

Explanation

To solve the problem, we need to understand how the transformation of the function \( g(x) \) to \( g(x-3) \) affects its graph.

### Step-by-Step Solution:

1. **Identify the Function**:
Let's consider a simple quadratic function for \( g(x) \). A common example is:
\[ g(x) = x^2 \]

2. **Transform the Function**:
We need to find \( g(x-3) \). Substituting \( x-3 \) into the function gives:
\[ g(x-3) = (x-3)^2 \]

3. **Expand the Transformed Function**:
Expanding \( g(x-3) \):
\[ g(x-3) = (x-3)(x-3) = x^2 - 6x + 9 \]

4. **Graphing the Functions**:
- The graph of \( g(x) = x^2 \) is a parabola that opens upwards with its vertex at the origin (0,0).
- The graph of \( g(x-3) = (x-3)^2 \) is also a parabola that opens upwards, but its vertex is now at the point (3,0).

5. **Determine the Relationship**:
The graph of \( g(x-3) \) is a horizontal shift of the graph of \( g(x) \) to the right by 3 units.

### Conclusion:
Thus, the relationship between the graphs of \( g(x) \) and \( g(x-3) \) is that the graph of \( g(x) \) is shifted 3 units to the right to obtain the graph of \( g(x-3) \).

### Final Answer:
The graph of \( g(x) \) is 3 units to the right of the graph of \( g(x-3) \).

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