Question 267977
Because {{{abs(y)<=2}}} and {{{abs(x)=abs(y)}}}, this means that {{{abs(x)<=2}}} as well. Why? Well say {{{x=3}}} (a value greater than 2), then {{{abs(3)=abs(y)}}} which would mean that {{{abs(y)>2}}} also. But this is a clear violation of the statement {{{abs(y)<=2}}}.



Since {{{abs(x)<=2}}}, this means that the only allowable "input" are values of {{{x}}} that satisfy the inequality {{{abs(x)<=2}}} since this is basically the conditions imposed on 'x'. Solve this inequality to get {{{-2<=x<=2}}}



So the domain is {{{-2<=x<=2}}} which in interval notation is *[Tex \LARGE \left\[-2,2\right\]]



Now take {{{abs(x)=abs(y)}}} and solve for 'y' to get {{{y=x}}} or {{{y=-x}}}. These equations are simply lines.


Now draw a vertical line through any random point on the circle. Does this line cut through more than one point? Barring one exception, the answer will be 'yes'. Since this is the case, the relation fails the vertical line test which means that this relation is NOT a function.