Graph the equation shown below by transforming the given graph of the parent function. \[ y=\sqrt[3]{-x} \]

To graph the equation \( y = \sqrt[3]{-x} \) by transforming the graph of the parent function \( y = \sqrt[3]{x} \), we can follow these steps: 1. **Identify the Parent Function**: The parent function is \( y = \sqrt[3]{x} \). This function has the following characteristics: - It passes through the origin (0,0). - It is an odd function, meaning it is symmetric about the origin. - As \( x \) approaches positive infinity, \( y \) also approaches positive infinity, and as \( x \) approaches negative infinity, \( y \) approaches negative infinity. 2. **Transform the Parent Function**: The equation \( y = \sqrt[3]{-x} \) can be interpreted as a transformation of the parent function: - The negative sign in front of \( x \) indicates a reflection across the y-axis. 3. **Graph the Transformed Function**: - Start with the graph of \( y = \sqrt[3]{x} \). - Reflect this graph across the y-axis to obtain the graph of \( y = \sqrt[3]{-x} \). ### Key Points: - The point (0, 0) remains unchanged. - The point (1, 1) on the parent function will reflect to (-1, 1). - The point (-1, -1) on the parent function will reflect to (1, -1). ### Summary of Points: - (0, 0) - (1, 1) transforms to (-1, 1) - (-1, -1) transforms to (1, -1) ### Final Graph: The graph of \( y = \sqrt[3]{-x} \) will look like the graph of \( y = \sqrt[3]{x} \) but reflected across the y-axis. It will still pass through the origin and will have the same general shape, but it will be oriented in the opposite direction along the x-axis. ### Visual Representation: To visualize this, you can sketch the graph by plotting the key points and drawing a smooth curve through them, ensuring that the curve is symmetric about the origin. The graph will extend into the first quadrant and third quadrant, reflecting the odd function property.