Question

The graph of f(x) = x² was transformed to create a graph g(x) =f(x)−3. Which statement about the graphs is true?

A) The vertex of the graph of g is 3 units above the vertex of the graph of f.
B) The vertex of the graph of g is 3 units below the vertex of the graph of f.
C) The vertex of the graph of g is 3 units to the left of the vertex of the graph of f.
D) The vertex of the graph of g is 3 units to the right of the vertex of the graph of f.

Answer 1

The correct statement is B) "The vertex of the graph of g is 3 units below the vertex of the graph of f."

1. Original Function:
`f(x) = x^2`

- The vertex of f(x) is at the origin, (0, 0).

2. Transformed Function: g(x) = f(x) - 3

- Subtracting 3 from f(x) shifts the entire graph downward by 3 units.

3. Vertex of g(x):

- The new vertex is located 3 units below the original vertex.

- So, the vertex of g(x) is (0, -3).

4. Conclusion:

- Option B) "The vertex of the graph of g is 3 units below the vertex of the graph of f" is correct.

In summary, subtracting a constant from the function shifts the graph downward, and in this case, it results in a new vertex for g(x) at (0, -3), making option B the accurate statement.