Question

determine if the relation defines y as a one-to-one function of x.

image of a coordinate grid with points plotted

options:
○ no
○ yes

Explanation:

Step1: Recall one - to - one function test

A function is one - to - one if it passes the horizontal line test. The horizontal line test states that if any horizontal line intersects the graph of the function more than once, then the function is not one - to - one. Also, first, we can check if it is a function using the vertical line test (a relation is a function if no vertical line intersects the graph more than once).
Looking at the given graph (from the points plotted), we observe the y - values. There are two different x - values that have the same y - value. For example, from the grid, we can see that when we draw a horizontal line, it will intersect the graph at more than one point (since there are points with the same y - coordinate but different x - coordinates).

Step2: Apply horizontal line test

Since there exist horizontal lines that intersect the graph of the relation more than once, the relation does not define a one - to - one function.

Answer:

No