Question
What is the vertical shift in f(x)=log
2
(−
128
x
) as compared to its parent function?
A. 7 units down
B. 7 units up
C. 2 units down
D. 2 units up
2
(−
128
x
) as compared to its parent function?
A. 7 units down
B. 7 units up
C. 2 units down
D. 2 units up
Answers
Answered by
GPT-4o mini
To analyze the vertical shift of the function \( f(x) = \log_2(-128x) \) compared to its parent function \( g(x) = \log_2(x) \), we need to recognize that the parent function has no vertical shift; its graph passes through the origin (0,0).
The function \( f(x) \) does not have an explicit vertical shift term in the form \( g(x) + k \) (where \( k \) would represent the vertical shift). Instead, it is a transformation of the logarithmic function in terms of its input.
Since the expression inside the log function is being multiplied by a negative constant and changed in terms of domain (the argument of the logarithm must be positive), there is no additional vertical translation involved in this function compared to the parent function itself.
Thus, we can conclude that there is no vertical shift in the function \( f(x) = \log_2(-128x) \) relative to the parent function \( g(x) = \log_2(x) \). However, since the given options suggest there is a vertical shift, it could imply exploring a different context or aspect.
Since none of the given options directly correspond to our conclusion of no vertical shift, please verify if there are additional details or corrections that might relate to these answer choices.
The function \( f(x) \) does not have an explicit vertical shift term in the form \( g(x) + k \) (where \( k \) would represent the vertical shift). Instead, it is a transformation of the logarithmic function in terms of its input.
Since the expression inside the log function is being multiplied by a negative constant and changed in terms of domain (the argument of the logarithm must be positive), there is no additional vertical translation involved in this function compared to the parent function itself.
Thus, we can conclude that there is no vertical shift in the function \( f(x) = \log_2(-128x) \) relative to the parent function \( g(x) = \log_2(x) \). However, since the given options suggest there is a vertical shift, it could imply exploring a different context or aspect.
Since none of the given options directly correspond to our conclusion of no vertical shift, please verify if there are additional details or corrections that might relate to these answer choices.