Consider the equation x^+ (y-2)^ = 1 and the relation “(x, y) R (0, 2)”, where R is read as “has distance 1 of”.

Consider the equation x^+ (y-2)^ = 1 and the relation “(x, y) R (0, 2)”, where R is read

as “has distance 1 of”.

For example, “(0, 3) R (0, 2)”, that is, “(0, 3) has distance 1 of (0, 2)”. This relation can

also be read as “the point (x, y) is on the circle of radius 1 with center (0, 2)”. In other

words: “(x, y) satisfies this equation, x^+ (y-2)^ = 1 if and only if, (x, y) R (0, 2)”. +




Does this equation determine a relation between x and y? Can the variable x can be seen

as a function of y, like x=g(y)? Can the variable y be expressed as a function of x, like y=

h(x)? If these are possible, then what will be the domains for these two functions? What

are the graphs of these two functions?

Are there points of the coordinate axes that relate to (0, 2) by means of R?




“A relation between two sets is a collection of ordered pairs containing one object from each

set. If the object x is from the first set and the object y is from the second set, then the objects

are said to be related if the ordered pair (x, y) is in the relation” (Nykamp, 2020). The

following table and mapping diagram shows the relationship between x and y. In

Mathematics, this relationship is also known as many - many relations.