A relationship between two values can be called a function if every input value produces exactly one output value - in other words, if a function [tex]f[/tex] takes in some number [tex]x[/tex] as input, every value of [tex]x[/tex] will produce a single value [tex]f(x)[/tex] as its output. Multiple [tex]x[/tex] values might produce the same [tex]f(x)[/tex], but no one [tex]x[/tex] value will produce more than one [tex]f(x)[/tex] value.
Here, we can see that the graphs b) and d) capture this kind of relationship, as each value on the [tex]x[/tex] axis is associated with one unique point on the graph. a) interestly enough, can be thought of a function, too; if we describe [tex]x[/tex] as a function of [tex]y[/tex], then every [tex]y[/tex] value produces exactly one [tex]x[/tex] value. The relationship captured in c) can't be interpreted as a function in either direction, though.
I assume this question is asking for [tex]y[/tex] as a function of [tex]x[/tex] though, in which case options b) and d) will be the correct response.
