Horizontal Line Test
The horizontal line test is a convenient method that can determine if the inverse of a function is also a function.
It is possible that the inverse of a function is not a function because it doesn’t pass the vertical line test.
So here’s the deal!
If the horizontal line intersects the graph of a function in all places at exactly one point, then the given function has an inverse that is also a function. We say this function passes the horizontal line test.
Here are some examples of functions that pass the horizontal line test:
Horizontal Line Cutting or Hitting the Graph at Exactly One Point
- Graph of the line f\left( x \right) = - x + 2.

- Graph of the square root function f\left( x \right) = \sqrt {x + 1}

- Graph of the rational function \large{f\left( x \right) = {1 \over {x + 1}}}.

On the other hand, if the horizontal line can intersect the graph of a function in some places at more than one point, then the function involved can’t have an inverse that is also a function.
We say this function fails the horizontal line test.
Here are some examples of functions that fail the horizontal line test:
Horizontal Line Cutting or Hitting the Graph at More Than One Point
- Graph of the parabola f\left( x \right) = {x^2} - 2.

- Graph of absolute value function f\left( x \right) = \left| x \right|

- Graph of semi-circle f\left( x \right) = \sqrt {7 - {x^2}}

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