algebra 2\nunit 1 topic 1: inverse relationships\ndate: 9/25/12\nis your original word a function? explain…

Explanation:

Step1: Recall function - definition

A relation is a function if for every x - value there is exactly one y - value. Use the vertical line test on the graph of the original relation.

Step2: Apply vertical line test

If a vertical line intersects the graph of the original relation at more than one point, then the original relation is not a function. If it intersects at most one point for every vertical line, then it is a function.

Step3: Recall inverse - function definition

The inverse of a relation is a function if the original relation passes the horizontal line test (for every y - value in the original relation, there is exactly one x - value).

Step4: Apply horizontal line test

If a horizontal line intersects the graph of the original relation at more than one point, then the inverse of the relation is not a function. If it intersects at most one point for every horizontal line, then the inverse is a function.

Answer:

To determine if the original relation is a function, apply the vertical line test. If any vertical line intersects the graph of the original relation at more than one point, the answer is "No, the original relation is not a function because it fails the vertical line test." If no vertical line intersects the graph at more than one point, the answer is "Yes, the original relation is a function because it passes the vertical line test." To determine if the inverse of the relation is a function, apply the horizontal line test to the original relation. If any horizontal line intersects the graph of the original relation at more than one point, the answer is "No, the inverse of the relation is not a function because the original relation fails the horizontal line test." If no horizontal line intersects the graph at more than one point, the answer is "Yes, the inverse of the relation is a function because the original relation passes the horizontal line test."