Inverses
Inverses
Quadratic Functions
A one-to-one function passes the horizontal line test as well as the vertical line test. In the graph of a function, no vertical line can pass through more than one point. In order to be a one-to-one function the same also has to be true for horizontal lines. No horizontal line can pass through more than one point of the graph.
The horizontal line test states: if any horizontal line intersects the graph of a function more than once, then the function does not have an inverse that is also a function.
Below are the graphs of y = x2 and x = y2:
The graph of y = x 2 does not pass the horizontal line test so its inverse, x = y 2 is not a function. The graph of x = y 2 does not pass the vertical line test, so it verifies that the horizontal line test on the original function works. Therefore, the graph of f(x) = x 2 shows that Quadratic functions have inverse relations, but their inverses are not functions.