Estrada Kelley
08/08/2024 · Middle School
Write an equation of the function \( g(x) \) that is the graph of \( f(x)=|x| \), but shifted right 4 units and shifted down 4 units.
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Step-by-step Solution
To find the equation of the function \( g(x) \) that represents the graph of \( f(x) = |x| \) shifted right 4 units and down 4 units, we can follow these steps:
1. **Shift Right 4 Units**: To shift the graph of \( f(x) \) to the right by 4 units, we replace \( x \) with \( x - 4 \). This gives us:
\[
f(x - 4) = |x - 4|
\]
2. **Shift Down 4 Units**: To shift the graph down by 4 units, we subtract 4 from the entire function. This results in:
\[
g(x) = |x - 4| - 4
\]
Putting it all together, the equation of the function \( g(x) \) is:
\[
g(x) = |x - 4| - 4
\]
Quick Answer
\( g(x) = |x - 4| - 4 \)
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