Question
Which of the following best describes the transformation that occurs when changing an equation from f(x)=x2+1
to f(x)=(x−3)2+1
?(1 point)
Responses
The graphed function would shift 3 units to the right but otherwise have the same shape.
The graphed function would shift 3 units to the right but otherwise have the same shape.
The graphed function would shift 3 units to the left and would be half as wide.
The graphed function would shift 3 units to the left and would be half as wide.
The graphed function would shift 3 units to the right and would be half as wide.
The graphed function would shift 3 units to the right and would be half as wide.
The graphed function would shift 3 units to the left but otherwise have the same shape.
to f(x)=(x−3)2+1
?(1 point)
Responses
The graphed function would shift 3 units to the right but otherwise have the same shape.
The graphed function would shift 3 units to the right but otherwise have the same shape.
The graphed function would shift 3 units to the left and would be half as wide.
The graphed function would shift 3 units to the left and would be half as wide.
The graphed function would shift 3 units to the right and would be half as wide.
The graphed function would shift 3 units to the right and would be half as wide.
The graphed function would shift 3 units to the left but otherwise have the same shape.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To analyze the transformation from the function \( f(x) = x^2 + 1 \) to \( f(x) = (x - 3)^2 + 1 \), we can consider how the components of the function change.
1. The original function \( f(x) = x^2 + 1 \) is a parabola that opens upwards with its vertex at the point (0, 1).
2. In the transformed function \( f(x) = (x - 3)^2 + 1 \), the term \( (x - 3) \) indicates a horizontal shift of the graph.
3. Specifically, the function \( (x - 3)^2 \) shifts the graph 3 units to the right compared to the original function, while the \( +1 \) maintains the same vertical position (the y-value doesn't change).
There are no changes to the width of the parabola since the coefficient of \( x^2 \) remains 1 in both cases.
Therefore, the correct response is:
**The graphed function would shift 3 units to the right but otherwise have the same shape.**
1. The original function \( f(x) = x^2 + 1 \) is a parabola that opens upwards with its vertex at the point (0, 1).
2. In the transformed function \( f(x) = (x - 3)^2 + 1 \), the term \( (x - 3) \) indicates a horizontal shift of the graph.
3. Specifically, the function \( (x - 3)^2 \) shifts the graph 3 units to the right compared to the original function, while the \( +1 \) maintains the same vertical position (the y-value doesn't change).
There are no changes to the width of the parabola since the coefficient of \( x^2 \) remains 1 in both cases.
Therefore, the correct response is:
**The graphed function would shift 3 units to the right but otherwise have the same shape.**
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