Question
The function f(x)=sinx is translated up 6 units. What is the minimum y value?
Answers
GPT-4o mini
To determine the minimum \( y \) value of the function \( f(x) = \sin x \) translated up by 6 units, we first need to find the minimum value of the original function.
The sine function, \( \sin x \), has a minimum value of \(-1\). When we translate a function upward by \( c \) units, we add \( c \) to the function. In this case, we are translating up by 6 units, so we modify the function as follows:
\[
g(x) = \sin x + 6
\]
Now, we calculate the minimum value of \( g(x) \). Since the minimum value of \( \sin x \) is \(-1\), we can find the minimum value of \( g(x) \):
\[
\text{Minimum value of } g(x) = -1 + 6 = 5
\]
Thus, the minimum \( y \) value of the translated function \( g(x) \) is
\[
\boxed{5}
\]
The sine function, \( \sin x \), has a minimum value of \(-1\). When we translate a function upward by \( c \) units, we add \( c \) to the function. In this case, we are translating up by 6 units, so we modify the function as follows:
\[
g(x) = \sin x + 6
\]
Now, we calculate the minimum value of \( g(x) \). Since the minimum value of \( \sin x \) is \(-1\), we can find the minimum value of \( g(x) \):
\[
\text{Minimum value of } g(x) = -1 + 6 = 5
\]
Thus, the minimum \( y \) value of the translated function \( g(x) \) is
\[
\boxed{5}
\]