Question
On a graph there is an upward v shape with points (-3,1),(-2,2),(-3,1),(-4,0),(-5,1),(-6,2),(-7,3)
Interpret the key features and type of transformation
Absolute value function has undergone a vertical translation
An absolute value function has undergone a horizontal translation
A quadratic function has undergone a vertical translation
A quadratic function has undergone a horizontal translation
Interpret the key features and type of transformation
Absolute value function has undergone a vertical translation
An absolute value function has undergone a horizontal translation
A quadratic function has undergone a vertical translation
A quadratic function has undergone a horizontal translation
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To analyze the given points and determine the type of function and its transformations, let's first identify the shape of the graph defined by these points:
The points are:
- (-3,1)
- (-2,2)
- (-4,0)
- (-5,1)
- (-6,2)
- (-7,3)
Plotting these points, we can see the upward and downward trends, suggesting the resemblance of an "upward V" shape, characteristic of an absolute value function.
### Characteristics of the Function:
1. **V-Shape**: The points (-3,1), (-2,2), and (-4,0) indicate that as you move away from the central point (-3,1), the function behaves symmetrically. This matches the behavior of the absolute value function which has a vertex, around which the points form a V shape.
2. **Vertex Location**: The vertex is at (-3, 1), which suggests that it has been translated vertically and horizontally.
### Transformation Analysis:
The standard absolute value function can be described by:
\[ f(x) = |x| \]
The general form for an absolute value function with transformations is:
\[ f(x) = a |x - h| + k \]
where (h, k) is the vertex of the "V".
### Identifying Vertical and Horizontal Translations:
From our identified vertex:
- **Horizontal Translation**: The graph has moved from the original position at the vertex of (0, 0) to (-3, 1). This shows that the graph has undergone a **horizontal translation to the left by 3 units**.
- **Vertical Translation**: The graph has also been translated up by 1 unit, as evident from the change in the y-coordinate.
### Conclusion:
Since the function matches the form of an absolute value function and has undergone both vertical and horizontal translations, the correct interpretation of the key features is that:
**An absolute value function has undergone both a vertical translation (upward by 1 unit) and a horizontal translation (to the left by 3 units).**
If you have to choose only one of the options given, the best fit would be:
- **An absolute value function has undergone a vertical translation** (since this emphasizes the vertical movement, but keep in mind that the horizontal translation is also significant).
The points are:
- (-3,1)
- (-2,2)
- (-4,0)
- (-5,1)
- (-6,2)
- (-7,3)
Plotting these points, we can see the upward and downward trends, suggesting the resemblance of an "upward V" shape, characteristic of an absolute value function.
### Characteristics of the Function:
1. **V-Shape**: The points (-3,1), (-2,2), and (-4,0) indicate that as you move away from the central point (-3,1), the function behaves symmetrically. This matches the behavior of the absolute value function which has a vertex, around which the points form a V shape.
2. **Vertex Location**: The vertex is at (-3, 1), which suggests that it has been translated vertically and horizontally.
### Transformation Analysis:
The standard absolute value function can be described by:
\[ f(x) = |x| \]
The general form for an absolute value function with transformations is:
\[ f(x) = a |x - h| + k \]
where (h, k) is the vertex of the "V".
### Identifying Vertical and Horizontal Translations:
From our identified vertex:
- **Horizontal Translation**: The graph has moved from the original position at the vertex of (0, 0) to (-3, 1). This shows that the graph has undergone a **horizontal translation to the left by 3 units**.
- **Vertical Translation**: The graph has also been translated up by 1 unit, as evident from the change in the y-coordinate.
### Conclusion:
Since the function matches the form of an absolute value function and has undergone both vertical and horizontal translations, the correct interpretation of the key features is that:
**An absolute value function has undergone both a vertical translation (upward by 1 unit) and a horizontal translation (to the left by 3 units).**
If you have to choose only one of the options given, the best fit would be:
- **An absolute value function has undergone a vertical translation** (since this emphasizes the vertical movement, but keep in mind that the horizontal translation is also significant).
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.