SOLUTION: X and Y are integers. Find the domain of the relation and draw it's graph. Is the relation a function? {(x,y): |x|=|y| and |y|≤ 2} Please Please help me.I'm begging. Thank

Algebra ->  Rational-functions -> SOLUTION: X and Y are integers. Find the domain of the relation and draw it's graph. Is the relation a function? {(x,y): |x|=|y| and |y|≤ 2} Please Please help me.I'm begging. Thank      Log On


   

Question 267977: X and Y are integers. Find the domain of the relation and draw it's graph. Is the relation a function?
{(x,y): |x|=|y| and |y|≤ 2}
Please Please help me.I'm begging.
Thank You!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Because abs%28y%29%3C=2 and abs%28x%29=abs%28y%29, this means that abs%28x%29%3C=2 as well. Why? Well say x=3 (a value greater than 2), then abs%283%29=abs%28y%29 which would mean that abs%28y%29%3E2 also. But this is a clear violation of the statement abs%28y%29%3C=2.


Since abs%28x%29%3C=2, this means that the only allowable "input" are values of x that satisfy the inequality abs%28x%29%3C=2 since this is basically the conditions imposed on 'x'. Solve this inequality to get -2%3C=x%3C=2


So the domain is -2%3C=x%3C=2 which in interval notation is


Now take abs%28x%29=abs%28y%29 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.