Question

{(-1,-3),(0,1),(3,-1),(4,-6)}
{(-1,-3),(0,1),(-1,-1),(4,-6)}
{(-1,-3),(0,1),(3,-1),(0,-6)}
{(-1,-3),(0,1),(4,-1),(4,-6)}

Which of the following represents a function

Answer 1

cartesian points are written in the form \[\huge (x,~y) \]

"A function is a relation for which each value from the set the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair." - http://tutorial.math.lamar.edu/Classes/Alg/FunctionDefn.aspx

This means that if something is a function: for every "x" value, there is only one possible "y" value

so check ur x values, see which ones appear twice, if there are 2 different y values for that x value - not a function

example:
line 3 above:
{(-1,-3),(0,1),(3,-1),(0,-6)}
\[ \large (-1,-3),~(\color {blue}{0}, \color {red}{1}),~(3,-1),~(\color {blue}{0},\color {red}{-6})\]
this line has the same x value appear twice : zero (the blue above)
but the corresponding y value for the 2 0's isn't the same (the red above)
one is 1, one is -6
if it was a function, it would only have the one value for this x value
\[\large therefore~line~3~is~\huge \color{red}{not} \large ~ a~ function\]