Question
Interpret the key features of the graph and identify the type of transformation that occurred. What
type of transformation occurred from the parent function?
Option #1: An absolute value function has undergone a vertical translation.
Option #2: An absolute value function has undergone a horizontal translation.
Option #3: A quadratic function has undergone a vertical translation.
Option #4: A quadratic function has undergone a horizontal translation
type of transformation occurred from the parent function?
Option #1: An absolute value function has undergone a vertical translation.
Option #2: An absolute value function has undergone a horizontal translation.
Option #3: A quadratic function has undergone a vertical translation.
Option #4: A quadratic function has undergone a horizontal translation
Answers
Answered by
GPT-4o mini
To interpret the key features of the graph and identify the type of transformation that occurred from the parent function, we need to consider some general aspects of transformations related to both absolute value and quadratic functions.
1. **Vertical Translation**:
- If a function undergoes a vertical translation, it means the graph has shifted up or down. This is typically indicated by adding or subtracting a constant to the function.
2. **Horizontal Translation**:
- A horizontal translation occurs when the graph shifts left or right. This is usually indicated by adding or subtracting a constant within the function's argument (for example, \( f(x - h) \) for right and \( f(x + h) \) for left).
3. **Absolute Value Functions**:
- The parent function for absolute value is \( f(x) = |x| \). A vertical translation would take the form \( f(x) = |x| + k \) (upward if \( k > 0 \), downward if \( k < 0 \)). A horizontal translation would take the form \( f(x) = |x - h| \) (right if \( h > 0 \), left if \( h < 0 \)).
4. **Quadratic Functions**:
- The parent function for quadratics is \( f(x) = x^2 \). A vertical translation takes the form \( f(x) = x^2 + k \) and a horizontal translation takes the form \( f(x) = (x - h)^2 \).
To accurately determine the type of transformation, we would typically examine the graph for features such as the vertex (the peak or trough of the graph), the direction it opens, or any shifts in its horizontal or vertical position.
Given the options provided and no specific graph to reference, the identification would depend on the originating parent function (absolute value or quadratic) and the observed shifts:
- If you see a vertex shifted up or down while the shape remains unchanged for an \( f(x) = |x| \) function, then it's a vertical translation.
- If the vertex moved left or right, it's a horizontal translation.
For a quadratic function, similar logic applies in identifying the up/down shift for a vertical translation and the left/right shift for a horizontal translation.
If you can relate your observed features to one of these transformations relative to the correct parent function, you can select the appropriate option:
1. If it's an absolute value function and it moved up or down: **Option #1**.
2. If it moved left or right: **Option #2**.
3. If it's a quadratic function and shifted up or down: **Option #3**.
4. If it shifted left or right: **Option #4**.
Please provide the specific graph features discussed to identify the correct transformation accurately.
1. **Vertical Translation**:
- If a function undergoes a vertical translation, it means the graph has shifted up or down. This is typically indicated by adding or subtracting a constant to the function.
2. **Horizontal Translation**:
- A horizontal translation occurs when the graph shifts left or right. This is usually indicated by adding or subtracting a constant within the function's argument (for example, \( f(x - h) \) for right and \( f(x + h) \) for left).
3. **Absolute Value Functions**:
- The parent function for absolute value is \( f(x) = |x| \). A vertical translation would take the form \( f(x) = |x| + k \) (upward if \( k > 0 \), downward if \( k < 0 \)). A horizontal translation would take the form \( f(x) = |x - h| \) (right if \( h > 0 \), left if \( h < 0 \)).
4. **Quadratic Functions**:
- The parent function for quadratics is \( f(x) = x^2 \). A vertical translation takes the form \( f(x) = x^2 + k \) and a horizontal translation takes the form \( f(x) = (x - h)^2 \).
To accurately determine the type of transformation, we would typically examine the graph for features such as the vertex (the peak or trough of the graph), the direction it opens, or any shifts in its horizontal or vertical position.
Given the options provided and no specific graph to reference, the identification would depend on the originating parent function (absolute value or quadratic) and the observed shifts:
- If you see a vertex shifted up or down while the shape remains unchanged for an \( f(x) = |x| \) function, then it's a vertical translation.
- If the vertex moved left or right, it's a horizontal translation.
For a quadratic function, similar logic applies in identifying the up/down shift for a vertical translation and the left/right shift for a horizontal translation.
If you can relate your observed features to one of these transformations relative to the correct parent function, you can select the appropriate option:
1. If it's an absolute value function and it moved up or down: **Option #1**.
2. If it moved left or right: **Option #2**.
3. If it's a quadratic function and shifted up or down: **Option #3**.
4. If it shifted left or right: **Option #4**.
Please provide the specific graph features discussed to identify the correct transformation accurately.