Wells Santiago
03/20/2023 · Elementary School
The function \( f(x)=x^{2} \), The graph of \( g(x) \) is \( f(x) \) translated to the left 6 units and down 5 units. What is the function rule for \( g(x) \) ? \( \begin{array}{l}g(x)=(x-6)^{2}+5 \\ g(x)=(x+6)^{2}-5 \\ \text { of } g(x)=(x+5)^{2}-6 \\ g(x)=(x-5)^{2}+6\end{array} \)
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Step-by-step Solution
To find the function rule for \( g(x) \), we need to consider the transformations applied to the function \( f(x) = x^2 \).
Given that the graph of \( g(x) \) is \( f(x) \) translated to the left 6 units and down 5 units, we can express this transformation in terms of the function rule for \( g(x) \).
The general form of a function after a horizontal translation \( h \) units to the left and a vertical translation \( k \) units down is given by:
\[ g(x) = f(x-h) + k \]
In this case, the function \( f(x) = x^2 \) is translated to the left 6 units and down 5 units. So, the function rule for \( g(x) \) is:
\[ g(x) = (x-6)^2 - 5 \]
Therefore, the correct function rule for \( g(x) \) is:
\[ g(x) = (x-6)^2 - 5 \]
Quick Answer
\[ g(x) = (x-6)^2 - 5 \]
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