Questions: Write the function whose graph is the graph of y=x but is shifted to the right 9 units. y= (Simplify your answer.)

Write the function whose graph is the graph of y=x but is shifted to the right 9 units. y= (Simplify your answer.)
Transcript text: Write the function whose graph is the graph of $y=|x|$ but is shifted to the right 9 units. \[ \mathrm{y}=\square \] (Simplify your answer.)
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Solution

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Solution Steps

Step 1: Identify the Base Function

The base function is $y = |x|$.

Step 2: Determine the Horizontal Shift

Graph is shifted 9 units right.

Step 3: Determine the Vertical Shift

No vertical shift.

Step 4: Substitute \(h\) and \(k\) into the General Form

The translated function is $f(x) = |x - (9)| + 0$.

Step 5: Calculate the Value of \(f(x)\) for a Given \(x\)-value

For \(x = 0\), \(f(x) = 9\).

Final Answer:

The value of the function at \(x = 0\) is \(f(x) = 9\).

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