Which relation does not represent a function? A) a vertical line B) y = 5 9 x - 3 C) a horizontal line D) {(1, 7), (3,7), (5, 7), (7,7)}

Answer: A) a vertical line does not represent a function. Step-by-step explanation: For a relation to be a function for each value of [tex]x[/tex] there must be only one value of [tex]y[/tex]. In other words a function is one in which each value in the domain set corresponds to only one value in the range set. Let us check for this condition in the give choices: A) a vertical line A vertical line is given as [tex]x=a[/tex] which meas it is parallel to y-axis and has infinite number of [tex]y[/tex] values for a single [tex]x[/tex] value.So, its  Not a function.  B) [tex]y=\frac{5}{9}x-3[/tex] For the given equation, on plugging in some [tex]x[/tex] value will give a single [tex]y[/tex] value. So, its a Function. C) a horizontal line A horizontal line is given as [tex]y=a[/tex] which meas it is parallel to x-axis and has infinite number of [tex]x[/tex] values giving a single [tex]y[/tex] value. So, its a  Function .D) {(1, 7), (3,7), (5, 7), (7,7)} For the given set for different [tex]x[/tex] valuesthere is only one [tex]y[/tex] value. So, its a  Function .