Questions: Graph the equation shown below by transforming the given graph of the parent function. y=4 sqrt(x-1)

Transcript text: Graph the equation shown below by transforming the given graph of the parent function. \[ y=4 \sqrt{x-1} \]

Solution

Solution Steps

Step 1: Identify the Parent Function

The parent function for the given equation \( y = 4\sqrt{x} - 1 \) is \( y = \sqrt{x} \).

Step 2: Apply Vertical Stretch

The coefficient 4 in \( y = 4\sqrt{x} - 1 \) indicates a vertical stretch by a factor of 4. This means that each y-coordinate of the parent function \( y = \sqrt{x} \) is multiplied by 4.

Step 3: Apply Vertical Shift

The term \(-1\) in \( y = 4\sqrt{x} - 1 \) indicates a vertical shift downward by 1 unit. This means that each y-coordinate of the vertically stretched function is decreased by 1.

Final Answer

The graph of the equation \( y = 4\sqrt{x} - 1 \) is obtained by vertically stretching the parent function \( y = \sqrt{x} \) by a factor of 4 and then shifting it downward by 1 unit. The resulting graph is shown in the image provided.

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