When an equation is graphed, we use the Vertical Line Test to determine if that equation is a function; if a vertical line hits more than one point anywhere on the graph, the graph is not a function.
This corresponds with the definition of a function: A function is a set of ordered pairs in which each element of the domain (x) is mapped to no more than one element of the range (y). Since every x has no more than one y, there will be no two points hit by the same vertical line.
When we have the graph of a function, to determine if it has an inverse, we use the Horizontal Line Test: if a horizontal line hits more than one point anywhere on the graph, the function does not have an inverse.
This corresponds with the definition of a one-to-one function: A function in which every element of the range (y) is mapped to exactly one element of the domain (x). Since every y has one x, there will be no horizontal line that hits more than one point anywhere on the graph.
<span>An inverse function is the relation formed when the independent variable is exchanged with the dependent variable in a given relation. To find this you just have to swap the x and y coordinates. The statement that could be used in this problem to explain why f(x) = 2x - 3 has an inverse relation that is a function is: B) f(x) is a one to one function.
