Question
What is the vertical shift in f(x)=log3(x681)
as compared to its parent function?
as compared to its parent function?
Answers
Answered by
GPT-4o mini
The parent function of the logarithm is \( f(x) = \log_b(x) \) for some base \( b \). In this case, the parent function is \( f(x) = \log_3(x) \).
The function you provided is \( f(x) = \log_3(x + 681) \).
To determine the vertical shift of \( f(x) = \log_3(x + 681) \) compared to its parent function \( f(x) = \log_3(x) \), we need to look at the argument of the logarithm.
The parent function \( \log_3(x) \) shifts to the left as we add a value inside the logarithm. Specifically, the function \( \log_3(x + 681) \) represents a horizontal shift (not a vertical shift). This function is shifted left by 681 units.
However, if you are considering the vertical shift, which involves adding a constant outside of the logarithm, we would write it in the form:
\[
f(x) = \log_3(x) + k
\]
If \( k \) is added, then it would represent a vertical shift. In this case, since no constant is added or subtracted outside the logarithm, the vertical shift is \( 0 \).
To summarize:
- The function \( f(x) = \log_3(x + 681) \) has a **horizontal shift of 681 units to the left**.
- The **vertical shift compared to the parent function** \( \log_3(x) \) is **0**.
The function you provided is \( f(x) = \log_3(x + 681) \).
To determine the vertical shift of \( f(x) = \log_3(x + 681) \) compared to its parent function \( f(x) = \log_3(x) \), we need to look at the argument of the logarithm.
The parent function \( \log_3(x) \) shifts to the left as we add a value inside the logarithm. Specifically, the function \( \log_3(x + 681) \) represents a horizontal shift (not a vertical shift). This function is shifted left by 681 units.
However, if you are considering the vertical shift, which involves adding a constant outside of the logarithm, we would write it in the form:
\[
f(x) = \log_3(x) + k
\]
If \( k \) is added, then it would represent a vertical shift. In this case, since no constant is added or subtracted outside the logarithm, the vertical shift is \( 0 \).
To summarize:
- The function \( f(x) = \log_3(x + 681) \) has a **horizontal shift of 681 units to the left**.
- The **vertical shift compared to the parent function** \( \log_3(x) \) is **0**.