The Inverse Function Line Test
A given graph represents a function only if for every value of x there is only one corresponding value of y.
This can be checked by using a vertical line and moving it through the x-axis. If that line intersects the graph more than once, then the graph does not correspond to a function.
The image shows a graph and if we move our imaginary vertical line from x=-2 to x=7 that line would intersect the graph only once. This means that the graph corresponds to a function in the domain [-2,7].
For the inverse function to exist, the horizontal line test must be passed.
Imagine a horizontal line moving through the y-axis. It would intersect the graph only once from y=0 to y=6.
We can conclude this graph corresponds to a function and it has an inverse function because it passed the horizontal line test.
Answer: D.
