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Use the graph of the function to answer the 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.

1 answer

To determine whether the function represented by the graph is a one-to-one function, we can use the Horizontal Line Test. A function is one-to-one if every horizontal line intersects the graph at most once.

Based on your description, the graph curves up to the right and down to the left, indicating that for certain ranges of y-values, there are x-values on both sides of the y-axis that result in the same y-value. For example, since it curves down towards the left through the point (-8, -2) and up to the right through (8, 2), a horizontal line at y = -2 and y = 2 would intersect the graph at more than one point.

Therefore, 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.