The **horizontal line test** is a convenient strategy that can recognize whether a provided feature has an inverse, yet even more importantly to uncover out if the inverse is additionally a duty.

You are watching: Horizontal line test vs vertical line test

Remember that it is extremely possible that a function may have an inverse yet at the same time, the inverse isnot a duty bereason it doesn’t pass the vertical line test.

So here’s the deal!

If the horizontal line intersects the graph of a duty in all locations **at exactly one point**, then the offered attribute must have actually an *inverse that is likewise a function*. We say this attribute **passes** the horizontal line test.

Here are some examples of attributes that pass the horizontal line test:

## Horizontal Line Cutting or Hitting the Graph at Exactly One Point

Graph of the line fleft( x ight) = - x + 2.

Graph of the square root attribute fleft( x ight) = sqrt x + 1

Graph of the rational functionlargefleft( x ight) = 1 over x + 1.

On the various other hand also, if the horizontal line have the right to intersect the graph of a role in some locations at **more than one point**, then the feature connected can’t have an inverse that is also a role.

We say this function falls short the horizontal line test.

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Here are some examples of features that **fail** the horizontal line test:

## Horizontal Line Cutting or Hitting the Graph at More Than One Point

Graph of the parabola fleft( x ight) = x^2 - 2.

Graph of absolute worth attribute fleft( x ight) = left| x ight|

Graph of semi-circle fleft( x ight) = sqrt 7 - x^2

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Vertical Line Test

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