Questions: Find the function that is finally graphed after the following transformations are applied to the graph of y=sqrt(x) in the order listed (1) Reflect about the x-axis (2) Shift up 4 units (3) Shift right 9 units

Find the function that is finally graphed after the following transformations are applied to the graph of y=sqrt(x) in the order listed (1) Reflect about the x-axis (2) Shift up 4 units (3) Shift right 9 units
Transcript text: Find the function that is finally graphed after the following transformations are applied to the graph of $y=\sqrt{x}$ in the order listed (1) Reflect about the $x$-axis (2) Shift up 4 units (3) Shift right 9 units
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Solution

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Solution Steps

Step 1: Reflect About the x-axis

The original function is given by

\[ y = \sqrt{x} \]

Reflecting this function about the \(x\)-axis involves negating the output:

\[ y = -\sqrt{x} \]

Step 2: Shift Up 4 Units

Next, we shift the graph up by 4 units. This is done by adding 4 to the function:

\[ y = -\sqrt{x} + 4 \]

This can also be expressed as:

\[ y = 4 - \sqrt{x} \]

Step 3: Shift Right 9 Units

Finally, we shift the graph to the right by 9 units. This is achieved by replacing \(x\) with \(x - 9\):

\[ y = 4 - \sqrt{x - 9} \]

Final Answer

The final function after all transformations is

\[ \boxed{y = 4 - \sqrt{x - 9}} \]

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