Write a formula for the function $g (x)$ obtained when the graph of $f (x) = | x |$ is shifted down 10 units and to the right 12 units.
Hint: You have a choice of two ways to enter your absolute value answer.
- If you use the "text" mode in Mobius (where the answer box is one line tall), then type in abs 0 for absolute value. For example, to enter $| x - 5 |$ type in abs(x-5).
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$g (x) =$

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Final Answer: The formula for the function $g (x)$ obtained when the graph of $f (x) = | x |$ is shifted down 10 units and to the right 12 units is $g (x) = | x - 12 | - 10$ .

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Step 1 ：The given function is $f (x) = | x |$ .

Step 2 ：When the graph of a function is shifted down by a units, the new function becomes $f (x) - a$ .

Step 3 ：When the graph of a function is shifted to the right by b units, the new function becomes $f (x - b)$ .

Step 4 ：So, when the graph of $f (x) = | x |$ is shifted down 10 units and to the right 12 units, the new function becomes $| x - 12 | - 10$ .

Step 5 ：Final Answer: The formula for the function $g (x)$ obtained when the graph of $f (x) = | x |$ is shifted down 10 units and to the right 12 units is $g (x) = | x - 12 | - 10$ .

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