Question 760528
A one to one function is a function in which every element in the range of the function corresponds with one and only one element in the domain.

    Example of a {{{one-to-one}}} function:

        { (0,1) , (5,2), (6,4) }
        Domain: 0, 5, 6
        Range: 1,2, 4

    Each element in the domain (0, 5, and 6) correspond with a unique element in the range. Therefore this function is a one-to-one function 


If a function is {{{one-to-one}}}, then the function not only passes the vertical line test (the vertical line test is a way to determine whether or not a relation is a function), but it also passes the {{{horizontal}}} line test.

    The Horizontal Line Test : 
If a horizontal line only intersects with the graph of a function once, then this function is {{{one-to-one}}}. If a horizontal line intersects the graph of the function more than once, then this function is not {{{one-to-one}}}. 

1. {{{2x - 5y =3}}}

{{{ graph( 600, 600, -10, 10, -10, 10, 3,3,(2/5)x-3/5) }}}

since a horizontal line only intersects with the graph of a function once, function is {{{one-to-one}}}

2. {{{y^2 - 3x + 7 =0}}}

{{{ graph( 600, 600, -10, 10, -10, 10, 3,3,sqrt(3x-7),-sqrt(3x-7)) }}}

since a horizontal line only intersects with the graph of a function once, function is {{{one-to-one}}}


3. {{{y= sqrt(5-2x)}}}

{{{ graph( 600, 600, -10, 10, -10, 10, 3,3,sqrt(5-2x),-sqrt(5-2x)) }}}

since a horizontal line only intersects with the graph of a function once, function is {{{one-to-one}}}

4. {{{y= x^3 -2}}}

{{{ graph( 600, 600, -10, 10, -10, 10, 3,3,x^3 -2) }}}

since a horizontal line only intersects with the graph of a function once, function is {{{one-to-one}}}


5. {{{y= x^2 -3x +2}}}

{{{ graph( 600, 600, -10, 10, -10, 10, 3,3,x^2 -3x +2) }}}

since a horizontal line intersects with the graph of a function twice, function is {{{NOT}}} {{{one-to-one}}}


6. {{{y= abs(3x-5)}}}

{{{ graph( 600, 600, -10, 10, -10, 10, 3,3, abs(3x-5)) }}}

since a horizontal line intersects with the graph of a function twice, function is {{{NOT}}} {{{one-to-one}}}