Questions: Graph the equation shown below by transforming the given function. y = sqrt(x+1) - 3

Graph the equation shown below by transforming the given function. y = sqrt(x+1) - 3
Transcript text: Graph the equation shown below by transforming the given function. \[ y=\sqrt{x+1}-3 \]
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Solution

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Solution Steps

Step 1: Identify the Parent Function

The parent function for the given equation \( y = \sqrt{x + 1} - 3 \) is \( y = \sqrt{x} \).

Step 2: Horizontal Shift

The term \( x + 1 \) inside the square root indicates a horizontal shift. Specifically, \( x + 1 \) means the graph of \( y = \sqrt{x} \) is shifted 1 unit to the left.

Step 3: Vertical Shift

The term \( -3 \) outside the square root indicates a vertical shift. Specifically, \( -3 \) means the graph is shifted 3 units down.

Final Answer

The graph of the equation \( y = \sqrt{x + 1} - 3 \) is obtained by taking the graph of the parent function \( y = \sqrt{x} \), shifting it 1 unit to the left, and then shifting it 3 units down.

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