Answer to Question #262755 in Calculus for Rye

Question

Describe the graph of a one-to-one function and its inverse?

Answer 1

A function is determined to be a one-to-one function by use of the horizontal line test on the graph of the function. If any horizontal line intersects the graph more than once, then the graph does not represent a one-to-one function.

A one-to-one function graph is one that any horizontal line intersects once as demonstrated below.

The inverse graph of a one-to-one function is plotted by switching all x and y values in each part of the graph. The values switch planes for the f(x) function to it's inverse g(x)(and back again), reflected on the line y=x.