Horizontal line test

A Horizontal line (y=c) can intersect the graph of f , a one-to-one function in at most one point .If intersects at more than one  point then it is not , one to one function .

So,   A function is one-to-one if and only if no horizontal line intersects its graph more than once.  Its called Horizontal line test.

Example 1: Is the function f(x)=x³   one-to-one?

Solution: Form the figure 3 we can see no horizontal line intersect the cube more than once.

Therefore , by Horizontal line test , f is one-to-one function  

Example 2: Is the function f(x)=x²  one-to-one?

Solution: Form the figure we can see  horizontal line intersect the cube more than once.

Therefore  , by Horizontal line test , f isn't one-to-one function