Questions: The image contains a grid or coordinate plane with x and y axes drawn on it. There are two intersecting lines plotted, forming what appears to be the graph of a linear or simple polynomial function.

The image contains a grid or coordinate plane with x and y axes drawn on it. There are two intersecting lines plotted, forming what appears to be the graph of a linear or simple polynomial function.

Transcript text: The image contains a grid or coordinate plane with x and y axes drawn on it. There are two intersecting lines plotted, forming what appears to be the graph of a linear or simple polynomial function.

Solution

Solution Steps

Step 1: Identify the Parent Function

The given function is \( y = \frac{4}{x} \). The parent function for this is \( y = \frac{1}{x} \).

Step 2: Determine the Transformation

The transformation involves multiplying the parent function by 4. This means the graph of \( y = \frac{1}{x} \) will be vertically stretched by a factor of 4.

Step 3: Apply the Transformation

To graph \( y = \frac{4}{x} \), take key points from the parent function \( y = \frac{1}{x} \) and multiply the y-values by 4. For example:

For \( x = 1 \), \( y = \frac{1}{1} = 1 \) becomes \( y = 4 \).
For \( x = -1 \), \( y = \frac{1}{-1} = -1 \) becomes \( y = -4 \).
For \( x = 2 \), \( y = \frac{1}{2} = 0.5 \) becomes \( y = 2 \).
For \( x = -2 \), \( y = \frac{1}{-2} = -0.5 \) becomes \( y = -2 \).

Final Answer

The graph of \( y = \frac{4}{x} \) is a vertical stretch of the graph of \( y = \frac{1}{x} \) by a factor of 4. The key points are transformed accordingly, and the graph maintains the same general shape but with y-values scaled by 4.

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