Question
Use the graph to answer the 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 is equal to open paren x plus 2 close paren squared. The equation of the transformed function is y is equal to x squared.
The parent function is y=x2
. The equation of the transformed function is y=(x+2)2
.
The parent function is y is equal to x squared. The equation of the transformed function is y is equal to open paren x plus 2 close paren squared.
The parent function is y=x2
. The equation of the transformed function is y=(x−2)2
.
The parent function is y is equal to x squared. The equation of the transformed function is y is equal to open paren x minus 2 close paren squared.
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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 is equal to open paren x plus 2 close paren squared. The equation of the transformed function is y is equal to x squared.
The parent function is y=x2
. The equation of the transformed function is y=(x+2)2
.
The parent function is y is equal to x squared. The equation of the transformed function is y is equal to open paren x plus 2 close paren squared.
The parent function is y=x2
. The equation of the transformed function is y=(x−2)2
.
The parent function is y is equal to x squared. The equation of the transformed function is y is equal to open paren x minus 2 close paren squared.
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Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine the parent function and the equation of the transformed function based on the graph, we need to identify the form of the transformation.
The parent function for a quadratic is generally given by the equation \(y = x^2\). If the graph shows a transformation, such as a horizontal shift to the left or right, it would be represented in the function as \(y = (x - h)^2\), where \(h\) indicates the horizontal shift.
Based on the typical transformations:
1. A leftward shift would be expressed as \(y = (x + k)^2\) for some \(k\).
2. A rightward shift would be expressed as \(y = (x - k)^2\).
If the function has been shifted left by 2 units, the equation would be \(y = (x + 2)^2\). If it has been shifted right by 2 units, it would be \(y = (x - 2)^2\).
Since the question mentions the options regarding the transformed function being in the form of \((x + 2)\) or \((x - 2)\), the correct choice will depend on the observed shift in the graph you referred to.
Given the choice options, it seems clear that:
- **The parent function is** \(y = x^2\).
- **If the graph represents a leftward shift by 2**, then the transformed function is \(y = (x + 2)^2\).
- **If the graph represents a rightward shift by 2**, then the transformed function is \(y = (x - 2)^2\).
From the responses provided:
- If the graph shows a left shift, the correct option is: *The parent function is \(y = x^2\). The equation of the transformed function is \(y = (x + 2)^2\).*
- If the graph shows a right shift, then the correct option is: *The parent function is \(y = x^2\). The equation of the transformed function is \(y = (x - 2)^2\).*
Please confirm the direction of the shift based on the graph to select the correct response!
The parent function for a quadratic is generally given by the equation \(y = x^2\). If the graph shows a transformation, such as a horizontal shift to the left or right, it would be represented in the function as \(y = (x - h)^2\), where \(h\) indicates the horizontal shift.
Based on the typical transformations:
1. A leftward shift would be expressed as \(y = (x + k)^2\) for some \(k\).
2. A rightward shift would be expressed as \(y = (x - k)^2\).
If the function has been shifted left by 2 units, the equation would be \(y = (x + 2)^2\). If it has been shifted right by 2 units, it would be \(y = (x - 2)^2\).
Since the question mentions the options regarding the transformed function being in the form of \((x + 2)\) or \((x - 2)\), the correct choice will depend on the observed shift in the graph you referred to.
Given the choice options, it seems clear that:
- **The parent function is** \(y = x^2\).
- **If the graph represents a leftward shift by 2**, then the transformed function is \(y = (x + 2)^2\).
- **If the graph represents a rightward shift by 2**, then the transformed function is \(y = (x - 2)^2\).
From the responses provided:
- If the graph shows a left shift, the correct option is: *The parent function is \(y = x^2\). The equation of the transformed function is \(y = (x + 2)^2\).*
- If the graph shows a right shift, then the correct option is: *The parent function is \(y = x^2\). The equation of the transformed function is \(y = (x - 2)^2\).*
Please confirm the direction of the shift based on the graph to select the correct response!
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