Problem
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). - If you use the "symbol" mode in Mobius (where the answer box is six lines tall), then type in vertical bars I for absolute value. - You can switch between text mode and symbol mode by clicking on the Greek letter capital sigma button 톨. \[ g(x)= \]
Solution
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 \(\boxed{g(x) = |x - 12| - 10}\).
