Question
The graphs below shows g(x) , which is a translation of a parent function f(x) . Write the function rule for g(x) . squiggle moved up 3
Answers
Answered by
GPT-4o mini
To write the function rule for \( g(x) \) as a translation of the parent function \( f(x) \), we need to consider what type of transformation is applied to \( f(x) \).
If the description states that the graph has "moved up 3," this means that we are performing a vertical translation. Specifically, we are shifting the graph of the function \( f(x) \) upward by 3 units.
The general rule for translating a function \( f(x) \) vertically up by \( k \) units is given by:
\[
g(x) = f(x) + k
\]
In your case, since the graph has moved up 3 units, \( k = 3 \). Therefore, the function rule for \( g(x) \) would be:
\[
g(x) = f(x) + 3
\]
If you have a specific parent function \( f(x) \) (e.g., \( f(x) = x^2 \) for a quadratic function), you can substitute that into the equation. For example, if \( f(x) = x^2 \), the function rule for \( g(x) \) would be:
\[
g(x) = x^2 + 3
\]
Please replace \( f(x) \) with the relevant parent function as needed!
If the description states that the graph has "moved up 3," this means that we are performing a vertical translation. Specifically, we are shifting the graph of the function \( f(x) \) upward by 3 units.
The general rule for translating a function \( f(x) \) vertically up by \( k \) units is given by:
\[
g(x) = f(x) + k
\]
In your case, since the graph has moved up 3 units, \( k = 3 \). Therefore, the function rule for \( g(x) \) would be:
\[
g(x) = f(x) + 3
\]
If you have a specific parent function \( f(x) \) (e.g., \( f(x) = x^2 \) for a quadratic function), you can substitute that into the equation. For example, if \( f(x) = x^2 \), the function rule for \( g(x) \) would be:
\[
g(x) = x^2 + 3
\]
Please replace \( f(x) \) with the relevant parent function as needed!