Questions: A function f is given, and the indicated transformation is applied to its graph. Write the equation for the final transformed graph f(x)=sqrt(x); shift 6 units to the left y=

A function f is given, and the indicated transformation is applied to its graph. Write the equation for the final transformed graph f(x)=sqrt(x); shift 6 units to the left y=
Transcript text: A function $f$ is given, and the indicated transformation is applied to its graph. Write the equation for the final transformed graph $f(x)=\sqrt{x}$; shift 6 units to the left \[ y= \]
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Solution

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Solution Steps

Step 1: Identify the Original Function

The original function given is \( f(x) = \sqrt{x} \).

Step 2: Apply the Horizontal Shift

To shift the graph of the function 6 units to the left, we replace \( x \) with \( x + 6 \) in the function. This results in the transformed function:

\[ f(x) = \sqrt{x + 6} \]

Final Answer

The equation for the final transformed graph is:

\[ \boxed{y = \sqrt{x + 6}} \]

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