Which transformation of a function's graph represents the inverse of the function? A Rotation of 90^circ about the origin B Reflection across the origin C Reflection across the line y=x (D) Reflection across the y-axis

To determine which transformation of a function's graph represents the inverse of the function, we need to understand the relationship between a function and its inverse.The inverse of a function is obtained by swapping the x-coordinates and y-coordinates of each point on the original function's graph. This means that if the original function is represented by the equation y = f(x), then the inverse function will be represented by the equation x = f(y).Now let's analyze each option:A) Rotation of about the origin: This transformation would not preserve the relationship between x and y, so it does not represent the inverse of the function.B) Reflection across the origin: This transformation would also not preserve the relationship between x and y, so it does not represent the inverse of the function.C) Reflection across the line : This transformation would swap the x-coordinates and y-coordinates of each point on the original function's graph, which is exactly what we need to obtain the inverse function. Therefore, this option represents the inverse of the function.D) Reflection across the y-axis: This transformation would not preserve the relationship between x and y, so it does not represent the inverse of the function.Therefore, the correct answer is C) Reflection across the line .