why is the graph of an inverse flipped over the line y=x instead of another line?
The inverse function of f(x) tells you what value of x you get for a given value of y. When you flip the graph about the 45 degree y=x line, it is the same as using the value of y on the original f(x) graph to get the value of x. In the flipped graph, what was formerly the y value is measured along the horizontal axis.
Why is the graph of an inverse of a function flipped over the line y = x instead of another line?
To understand why the graph of an inverse is flipped over the line y=x instead of another line, we need to understand the concept of an inverse function and how it relates to the original function.
When you have a function f(x), it maps each input value x to a unique output value y. In other words, for every x in the domain of f, there is a unique y in the range of f.
Now, the inverse function of f, denoted as f^(-1), does the opposite. It takes an output value y and returns the corresponding input value x. In other words, for every y in the range of f, there is a unique x in the domain of f.
To obtain the graph of the inverse function, we can switch the x and y coordinates of each point on the graph of the original function f(x). This is done by reflecting the points over the line y=x.
Why do we specifically choose the line y=x for this reflection? It is because the line y=x represents a symmetry line for the original function. When we flip the graph of f(x) over the line y=x to obtain the graph of f^(-1), we are essentially swapping the input values (x) with the output values (y).
By flipping the graph over the line y=x, the x-coordinate of each point in the original graph becomes the y-coordinate in the inverse graph, and vice versa. This ensures that the relationship between the input and output values is preserved.
Therefore, the graph of the inverse function is flipped over the line y=x, rather than another line, because it allows us to obtain a function that accurately represents the inverse relationship between the x and y values of the original function.