Asked by puplic safter rules
The graph of f(x) = x2 was transformed to create a graph g(x) =f(x)−6.
Which statement about the graphs is true?
Responses
The vertex of the graph of g is 6 units below the vertex of the graph of f.
The vertex of the graph of g is 6 units below the vertex of the graph of f.
The vertex of the graph of g is 6 units above the vertex of the graph of f.
The vertex of the graph of g is 6 units above the vertex of the graph of f.
The vertex of the graph of g is 6 units to the left of the vertex of the graph of f.
The vertex of the graph of g is 6 units to the left of the vertex of the graph of f.
The vertex of the graph of g is 6 units to the right of the vertex of the graph of f.
Which statement about the graphs is true?
Responses
The vertex of the graph of g is 6 units below the vertex of the graph of f.
The vertex of the graph of g is 6 units below the vertex of the graph of f.
The vertex of the graph of g is 6 units above the vertex of the graph of f.
The vertex of the graph of g is 6 units above the vertex of the graph of f.
The vertex of the graph of g is 6 units to the left of the vertex of the graph of f.
The vertex of the graph of g is 6 units to the left of the vertex of the graph of f.
The vertex of the graph of g is 6 units to the right of the vertex of the graph of f.
Answers
Answered by
GPT-4o mini
To analyze the transformation from \( f(x) = x^2 \) to \( g(x) = f(x) - 6 = x^2 - 6 \), we need to identify how the graph is being shifted.
The vertex of the graph of \( f(x) = x^2 \) is at the point \( (0, 0) \).
When we create \( g(x) = x^2 - 6 \), this represents a vertical shift of the entire graph of \( f(x) \) downward by 6 units.
Therefore, the vertex of \( g(x) \) will be at the point \( (0, -6) \).
Given this transformation, we can summarize the following:
- The vertex of the graph of \( g \) is **6 units below** the vertex of the graph of \( f \).
Thus, the correct statement is:
**The vertex of the graph of g is 6 units below the vertex of the graph of f.**
The vertex of the graph of \( f(x) = x^2 \) is at the point \( (0, 0) \).
When we create \( g(x) = x^2 - 6 \), this represents a vertical shift of the entire graph of \( f(x) \) downward by 6 units.
Therefore, the vertex of \( g(x) \) will be at the point \( (0, -6) \).
Given this transformation, we can summarize the following:
- The vertex of the graph of \( g \) is **6 units below** the vertex of the graph of \( f \).
Thus, the correct statement is:
**The vertex of the graph of g is 6 units below the vertex of the graph of f.**