Questions: Which of the following functions has a graph that is the graph of y=sqrt(x) shifted down 4 units? Choose the correct answer below. y=sqrt(x+4) y=sqrt(x-4) y=sqrt(x)-4 y=sqrt(x)+4

Which of the following functions has a graph that is the graph of y=sqrt(x) shifted down 4 units? Choose the correct answer below. y=sqrt(x+4) y=sqrt(x-4) y=sqrt(x)-4 y=sqrt(x)+4
Transcript text: Which of the following functions has a graph that is the graph of $y=\sqrt{x}$ shifted down 4 units? Choose the correct answer below. $y=\sqrt{x+4}$ $y=\sqrt{x-4}$ $y=\sqrt{x}-4$ $y=\sqrt{x}+4$
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Solution

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Solution Steps

To determine which function represents the graph of \( y = \sqrt{x} \) shifted down 4 units, we need to understand how vertical shifts affect the graph of a function. A vertical shift down by 4 units means we subtract 4 from the original function.

Step 1: Identify the Original Function

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

Step 2: Determine the Transformation

To shift the graph of \( y = \sqrt{x} \) down by 4 units, we subtract 4 from the original function. This results in the new function: \[ y = \sqrt{x} - 4 \]

Final Answer

\(\boxed{y = \sqrt{x} - 4}\)

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