Question

Using the horizontal line test, which of the following can be concluded about

Answer 1

Step-by-step answer:

A vertical line test checks for single or multiple intersections with a given relations  If there is a maximum of one intersection with the relation at ANY point in the domain of the relation, we can conclude that the relation is a function.  If there are multiple intersections of a VERTICAL line with the function, it is not a function.

Here, we see that vertical line test on the relation shown does not produce more than one intersection at any point in the domain of the relation, hence we conclude that the graph shows a function.

An inverse of a function is a reflection of the function about the y=x line.  The result is the same as the interchange of the x and y-axes.

Hence a horizontal line test on the inverse of a function gives the same results as a vertical line test of the function itself, and the conclusion is identical to the test given above in paragraph two.