Question 5 of 8 Use the drawing tools to form the correct answer on the graph. What is the inverse of the function shown?

To determine the inverse of the function shown on the graph, you can follow these general steps. Since I don't have access to the specific graph you're referencing, I'll outline the standard method to find an inverse function graphically: ### **1. Understand What an Inverse Function Is** The inverse of a function essentially "reverses" the original function. If the original function maps an input \( x \) to an output \( y \), the inverse function maps \( y \) back to \( x \). ### **2. Check If the Function Is Invertible** - **One-to-One Function:** Ensure that the original function is one-to-one (each \( y \) value corresponds to exactly one \( x \) value). This means the function passes the **Horizontal Line Test**—no horizontal line intersects the graph more than once.  ### **3. Reflect the Graph Over the Line \( y = x \)** - **Plot the Line \( y = x \):** Draw a 45-degree line passing through the origin where \( y = x \).  - **Reflect Each Point:** For every point \( (a, b) \) on the original function, plot the point \( (b, a) \) to get the inverse function.  ### **4. Draw the Inverse Function** After reflecting all relevant points, sketch the inverse function's curve based on these reflected points. ### **5. Verify by Swapping Variables Algebraically (If Possible)** If the function's equation is known, you can find the inverse algebraically: 1. Start with the original function's equation: \( y = f(x) \). 2. Swap \( x \) and \( y \): \( x = f(y) \). 3. Solve for \( y \) to get \( f^{-1}(x) \). **Example:** Suppose the original function is \( y = 2x + 3 \). 1. Swap \( x \) and \( y \): \( x = 2y + 3 \). 2. Solve for \( y \): \[ x - 3 = 2y \\ y = \frac{x - 3}{2} \] 3. So, the inverse function is \( y = \frac{x - 3}{2} \). ### **6. Use Graphing Tools** If you're using drawing tools: - **Draw the Line \( y = x \):** This will serve as the mirror line. - **Plot Key Points:** Identify and plot key points from the original function and reflect them over \( y = x \). - **Sketch the Inverse Function:** Connect the reflected points smoothly to form the inverse function. ### **Final Tips** - **Consistency:** Ensure that the inverse function accurately reflects the original function over the line \( y = x \). - **Label Clearly:** Clearly label both functions and the line \( y = x \) for clarity. If you can provide more details about the specific function or its graph, I can offer a more tailored explanation or verify the inverse for you!