Write a function based on the given parent function and transformations in the given ord Parent function: \( y=\frac{1}{x} \) (1) Stretch vertically by a factor of 7 . (2) Reflect across the \( x \)-axis. (3) Shift downward 2 units. Try again based on the given parent function and transformations in the given order

Certainly! Let's construct the transformed function step by step based on the given parent function and the specified transformations applied in the order provided. **Parent Function:** \[ y = \frac{1}{x} \] **Transformations:** 1. **Stretch Vertically by a Factor of 7:** - **Operation:** Multiply the function by 7. - **Resulting Function:** \[ y = 7 \cdot \frac{1}{x} = \frac{7}{x} \] 2. **Reflect Across the \( x \)-Axis:** - **Operation:** Multiply the function by -1. - **Resulting Function:** \[ y = -1 \cdot \frac{7}{x} = -\frac{7}{x} \] 3. **Shift Downward 2 Units:** - **Operation:** Subtract 2 from the function. - **Resulting Function:** \[ y = -\frac{7}{x} - 2 \] **Final Transformed Function:** \[ y = -\frac{7}{x} - 2 \] **Function Implementation:** If you want to implement this function in a programming language like Python, here's how you can do it: ```python def transformed_function(x): if x == 0: raise ValueError("x cannot be zero, as division by zero is undefined.") return -7 / x - 2 # Example usage: # print(transformed_function(1)) # Output: -9.0 # print(transformed_function(-1)) # Output: 5.0 ``` **Explanation:** 1. **Vertical Stretch by 7:** Multiplying by 7 makes the graph seven times "taller" than the parent function. 2. **Reflection Across the \( x \)-Axis:** Multiplying by -1 flips the graph over the \( x \)-axis. 3. **Downward Shift by 2 Units:** Subtracting 2 moves the entire graph down by 2 units on the \( y \)-axis. This sequence of transformations modifies the original hyperbola \( y = \frac{1}{x} \) to \( y = -\frac{7}{x} - 2 \), altering its orientation, size, and position on the coordinate plane.