Use the graph of the function to answer the question.

Question

Choose the statement that correctly describes the graph of the function and correctly explains the reasoning.
A graph is shown on the coordinate plane.

The x-axis goes from negative 10 to 10 and the y-axis goes from negative 10 to 10. From the origin, the graph curves up and to the right through point left-parenthesis 8 comma 2 right-parenthesis and continues to the right. From the origin the graph also curves down and the left through point left-parenthesis negative 8 comma negative 2 and continues left.
(1 point)
Responses

This is a one-to-one function because there exists a horizontal line that would intersect the graph of the function more than once.
This is a one-to-one function because there exists a horizontal line that would intersect the graph of the function more than once.

This is a one-to-one function because there is no horizontal line that would intersect the graph of the function more than once.
This is a one-to-one function because there is no horizontal line that would intersect the graph of the function more than once.

This is not a one-to-one function because there exists a horizontal line that would intersect the graph of the function more than once.
This is not a one-to-one function because there exists a horizontal line that would intersect the graph of the function more than once.

This is not a one-to-one function because there is no horizontal line that would intersect the graph of the function more than once.
This is not a one-to-one function because there is no horizontal line that would intersect the graph of the function more than once.
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Answer 1

Based on the description of the graph, the function appears to have both a part that curves upwards to the right and another that curves downwards to the left. The presence of points such as (8, 2) and (-8, -2) suggests that for certain y-values, there are multiple corresponding x-values (e.g., positive and negative x-values yielding the same y-value).

Given this information:

The correct statement is: This is not a one-to-one function because there exists a horizontal line that would intersect the graph of the function more than once.

This is because a one-to-one function must pass the horizontal line test, meaning that no horizontal line drawn should intersect the graph more than once; in this case, it intersects multiple times.