Question
Describe the transformation that occurred to the parent function f(x)=log2x
(1 point)
Responses
a vertical shrink by 12
a vertical shrink by 1 half
a reflection over the x-axis
a reflection over the x-axis
a shift right 3 units
a shift right 3 units
a shift down 3 units
(1 point)
Responses
a vertical shrink by 12
a vertical shrink by 1 half
a reflection over the x-axis
a reflection over the x-axis
a shift right 3 units
a shift right 3 units
a shift down 3 units
Answers
GPT-4o mini
To determine the transformation that occurred to the parent function \( f(x) = \log_2(x) \), we need context on the transformed function. However, based on the response options provided, here’s a breakdown of what each transformation means:
1. **A vertical shrink by \( \frac{1}{2} \)**: This means the function has been multiplied by a factor less than 1, resulting in the outputs being halved. For example, \( f(x) = \frac{1}{2} \log_2(x) \).
2. **A reflection over the x-axis**: This means the values of the function have been negated. For example, \( f(x) = -\log_2(x) \).
3. **A shift right 3 units**: This implies that the function \( f(x) \) has been modified to \( f(x) = \log_2(x - 3) \), shifting the graph to the right.
4. **A shift down 3 units**: This indicates that the function has been lowered by 3 units, represented as \( f(x) = \log_2(x) - 3 \).
Without a specific transformed function to analyze, it's not clear what transformation has actually occurred. Please provide the transformed function or name the transformation to clarify. If you need an example of which transformation might commonly apply to a function, just let me know!
1. **A vertical shrink by \( \frac{1}{2} \)**: This means the function has been multiplied by a factor less than 1, resulting in the outputs being halved. For example, \( f(x) = \frac{1}{2} \log_2(x) \).
2. **A reflection over the x-axis**: This means the values of the function have been negated. For example, \( f(x) = -\log_2(x) \).
3. **A shift right 3 units**: This implies that the function \( f(x) \) has been modified to \( f(x) = \log_2(x - 3) \), shifting the graph to the right.
4. **A shift down 3 units**: This indicates that the function has been lowered by 3 units, represented as \( f(x) = \log_2(x) - 3 \).
Without a specific transformed function to analyze, it's not clear what transformation has actually occurred. Please provide the transformed function or name the transformation to clarify. If you need an example of which transformation might commonly apply to a function, just let me know!