Question
The graph of a transformed function is shown. Determine the parent function and the equation of the transformed function.
(1 point)
Responses
The parent function is y=(x−2)2. The equation of the transformed function is y=x2
The parent function is y=(x+2)2. The equation of the transformed function is y=x2
The parent function is y=x2. The equation of the transformed function is y=(x−2)2
The parent function is y=x2. The equation of the transformed function is y=(x+2)2
(1 point)
Responses
The parent function is y=(x−2)2. The equation of the transformed function is y=x2
The parent function is y=(x+2)2. The equation of the transformed function is y=x2
The parent function is y=x2. The equation of the transformed function is y=(x−2)2
The parent function is y=x2. The equation of the transformed function is y=(x+2)2
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To identify the parent function and the equation of the transformed function accurately, it’s essential to examine any given transformations such as shifts, compressions/expansions, and reflections.
Since I can't see the graph, I'll provide guidance based on common transformations related to the standard parent function \(y = x^2\):
1. **Horizontal Shift**:
- If the graph is shifted to the right by 2 units, the equation becomes \(y = (x - 2)^2\).
- If the graph is shifted to the left by 2 units, the equation becomes \(y = (x + 2)^2\).
2. **Vertical Shift**:
- If there’s a vertical shift, you would add or subtract a constant to the entire function.
Assuming the graph represents a parabola that opens upwards and has been transformed from \(y = x^2\), we can analyze the options based on the transformations described:
- If the function appears to be shifted to the right (e.g., vertex at (2,0)), then the parent function is \(y = x^2\) and the transformed function is \(y = (x - 2)^2\).
- If the function appears to be shifted to the left (e.g., vertex at (-2,0)), then it would be \(y = (x + 2)^2\).
Therefore, without specific visual details, I'd recommend checking the location of the vertex and the symmetry of the parabola.
The most common transformation options are:
- **If shifted to the right by 2**:
- Parent function: \(y = x^2\)
- Transformed function: \(y = (x - 2)^2\)
- **If shifted to the left by 2**:
- Parent function: \(y = x^2\)
- Transformed function: \(y = (x + 2)^2\)
Based on these considerations, if the graph's vertex moves to the right, you should choose:
**The parent function is \(y = x^2\). The equation of the transformed function is \(y = (x - 2)^2\).**
If it's to the left, the appropriate answer would be:
**The parent function is \(y = x^2\). The equation of the transformed function is \(y = (x + 2)^2\).**
If you have another specific detail from the graph, that could help further narrow down the options.
Since I can't see the graph, I'll provide guidance based on common transformations related to the standard parent function \(y = x^2\):
1. **Horizontal Shift**:
- If the graph is shifted to the right by 2 units, the equation becomes \(y = (x - 2)^2\).
- If the graph is shifted to the left by 2 units, the equation becomes \(y = (x + 2)^2\).
2. **Vertical Shift**:
- If there’s a vertical shift, you would add or subtract a constant to the entire function.
Assuming the graph represents a parabola that opens upwards and has been transformed from \(y = x^2\), we can analyze the options based on the transformations described:
- If the function appears to be shifted to the right (e.g., vertex at (2,0)), then the parent function is \(y = x^2\) and the transformed function is \(y = (x - 2)^2\).
- If the function appears to be shifted to the left (e.g., vertex at (-2,0)), then it would be \(y = (x + 2)^2\).
Therefore, without specific visual details, I'd recommend checking the location of the vertex and the symmetry of the parabola.
The most common transformation options are:
- **If shifted to the right by 2**:
- Parent function: \(y = x^2\)
- Transformed function: \(y = (x - 2)^2\)
- **If shifted to the left by 2**:
- Parent function: \(y = x^2\)
- Transformed function: \(y = (x + 2)^2\)
Based on these considerations, if the graph's vertex moves to the right, you should choose:
**The parent function is \(y = x^2\). The equation of the transformed function is \(y = (x - 2)^2\).**
If it's to the left, the appropriate answer would be:
**The parent function is \(y = x^2\). The equation of the transformed function is \(y = (x + 2)^2\).**
If you have another specific detail from the graph, that could help further narrow down the options.
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