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The graph of a transformed function is shown. Determine the parent function and the equation of the transformed function. (1 po...Question
The graph of a transformed function is shown. Determine the parent function and the equation of the transformed function.
(1 point)
Responses
A. The parent function is y=(x−2)2. The equation of the transformed function is y=x2
B. The parent function is y=(x+2)2. The equation of the transformed function is y=x2
C. The parent function is y=x2. The equation of the transformed function is y=(x−2)2
D. The parent function is y=x2. The equation of the transformed function is y=(x+2)2
(1 point)
Responses
A. The parent function is y=(x−2)2. The equation of the transformed function is y=x2
B. The parent function is y=(x+2)2. The equation of the transformed function is y=x2
C. The parent function is y=x2. The equation of the transformed function is y=(x−2)2
D. The parent function is y=x2. The equation of the transformed function is y=(x+2)2
Answers
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Answered by
GPT-4o mini
To determine the parent function and the equation of the transformed function from the options provided, we need to analyze the transformations described in the equations involving the function \( y = x^2 \).
1. **Identify the parent function**: The parent function for a quadratic equation is \( y = x^2 \).
2. **Analyze transformations**:
- Transformation involving \( (x-2)^2 \) indicates a horizontal shift to the right by 2 units.
- Transformation involving \( (x+2)^2 \) indicates a horizontal shift to the left by 2 units.
Given the provided options:
- **A** suggests transforming \( (x-2)^2\) from \( y = x^2\).
- **B** suggests transforming \( (x+2)^2\) from \( y = x^2\).
- **C** suggests the inverse: transforming \( (x-2)^2\) which means the function starts as \( y = x^2\) before moving.
- **D** suggests \( (x+2)^2\) is transformed from \( y=x^2\).
To deduce correctly:
- If the transformed function is **\( y = (x - 2)^2 \)**, the parent function is **\( y = x^2 \)**.
- If the transformed function is **\( y = (x + 2)^2 \)**, the parent function is also **\( y = x^2 \)**.
The only correct match for identifying standard transformations practiced with parent functions while being tied to \( y = x^2 \) is option **C**.
Thus, the answer is:
**C. The parent function is \( y = x^2 \). The equation of the transformed function is \( y = (x - 2)^2 \)**.
1. **Identify the parent function**: The parent function for a quadratic equation is \( y = x^2 \).
2. **Analyze transformations**:
- Transformation involving \( (x-2)^2 \) indicates a horizontal shift to the right by 2 units.
- Transformation involving \( (x+2)^2 \) indicates a horizontal shift to the left by 2 units.
Given the provided options:
- **A** suggests transforming \( (x-2)^2\) from \( y = x^2\).
- **B** suggests transforming \( (x+2)^2\) from \( y = x^2\).
- **C** suggests the inverse: transforming \( (x-2)^2\) which means the function starts as \( y = x^2\) before moving.
- **D** suggests \( (x+2)^2\) is transformed from \( y=x^2\).
To deduce correctly:
- If the transformed function is **\( y = (x - 2)^2 \)**, the parent function is **\( y = x^2 \)**.
- If the transformed function is **\( y = (x + 2)^2 \)**, the parent function is also **\( y = x^2 \)**.
The only correct match for identifying standard transformations practiced with parent functions while being tied to \( y = x^2 \) is option **C**.
Thus, the answer is:
**C. The parent function is \( y = x^2 \). The equation of the transformed function is \( y = (x - 2)^2 \)**.
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