What test determines if a graph is a one-to-one function by using horizontal lines?

What test determines if a graph is a one-to-one function by using horizontal lines?

• A. Vertical line test
• B. Horizontal line test
• C. Reflection test
• D. Symmetry test

Answer: (B)

The horizontal line test is the appropriate method for determining if a graph represents a one-to-one function. This test states that a function is one-to-one if and only if no horizontal line intersects the graph at more than one point. If any horizontal line crosses the graph at multiple points, it indicates that there exist at least two different input values (x-values) yielding the same output value (y-value), thus confirming the function is not one-to-one. This is an important concept in identifying functions within mathematics, particularly when discussing invertibility and the relationship between input and output. A one-to-one function has unique outputs for every input, making it essential in many applications of mathematics. The vertical line test, in contrast, is used to determine whether a graph represents a function at all, specifically ensuring that for every x-value there is only one y-value. Reflection and symmetry tests focus more on the properties of the graphs concerning lines of symmetry, rather than the relationship between inputs and outputs.

The horizontal line test is the appropriate method for determining if a graph represents a one-to-one function. This test states that a function is one-to-one if and only if no horizontal line intersects the graph at more than one point. If any horizontal line crosses the graph at multiple points, it indicates that there exist at least two different input values (x-values) yielding the same output value (y-value), thus confirming the function is not one-to-one.

This is an important concept in identifying functions within mathematics, particularly when discussing invertibility and the relationship between input and output. A one-to-one function has unique outputs for every input, making it essential in many applications of mathematics.

The vertical line test, in contrast, is used to determine whether a graph represents a function at all, specifically ensuring that for every x-value there is only one y-value. Reflection and symmetry tests focus more on the properties of the graphs concerning lines of symmetry, rather than the relationship between inputs and outputs.