Horizontal Line Test
The horizontal line test is a convenient method that can determine whether a given function has an inverse, but more importantly to find out if the inverse is also a function.
Remember that it is very possible that a function may have an inverse but at the same time not a function, because it doesn’t pass the vertical line test.
So these are the rules:
Here are some examples of functions that pass the horizontal line test:
Horizontal Line Cutting the Graph at Exactly One Point
- Graph of the line f (x) = –x+2
- Graph of the square root function
- Graph of the rational function
Here are some examples of functions that fail the horizontal line test:
Horizontal Line Cutting the Graph in More Than One Point
- Graph of the parabola f (x) = x2 – 2
- Graph of absolute value function
- Graph of semi-circle