Question
The graph shows g(x), which is a translation of f(x)=|x|. Write the function rule for g(x). Write your answer in the form a|x–h|+k, where a, h, and k are integers or simplified fractions. went right 2
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g(x)=
Answers
GPT-4o mini
To write the function rule for \( g(x) \), which is a translation of \( f(x) = |x| \), we need to account for the translation mentioned.
The function \( f(x) = |x| \) is the absolute value function centered at the origin. The description states that \( g(x) \) translates \( f(x) \) to the right by 2 units.
To translate the graph of \( f(x) \) to the right by 2 units, we replace \( x \) with \( x - 2 \) in the function. Therefore, the function rule for \( g(x) \) becomes:
\[
g(x) = |x - 2|
\]
This is in the form \( a|x - h| + k \), where \( a = 1 \), \( h = 2 \), and \( k = 0 \).
Thus, the final answer is:
\[
g(x) = 1|x - 2| + 0
\]
To summarize, the function rule for \( g(x) \) is:
\[
g(x) = |x - 2|
\]
The function \( f(x) = |x| \) is the absolute value function centered at the origin. The description states that \( g(x) \) translates \( f(x) \) to the right by 2 units.
To translate the graph of \( f(x) \) to the right by 2 units, we replace \( x \) with \( x - 2 \) in the function. Therefore, the function rule for \( g(x) \) becomes:
\[
g(x) = |x - 2|
\]
This is in the form \( a|x - h| + k \), where \( a = 1 \), \( h = 2 \), and \( k = 0 \).
Thus, the final answer is:
\[
g(x) = 1|x - 2| + 0
\]
To summarize, the function rule for \( g(x) \) is:
\[
g(x) = |x - 2|
\]