ALgebra 2 Function and Relations

Find Domain and grah. Is relation a function? :

a.{(x,y): |x|=|y| and |x|<=|1}

b.{(x,y): |y|=x and x<=3}

c.{(x,y): |x|+|y|=2}

d.{(x,y): |x+y|=0 and |y|<=2}

e.{(x,y): |y|<=2}

Two functions are equal if they have the same ordered pair. f and g have the same domain D and range. Determine if f=g.

D={-2,-1,1,2} f: x --->4-x^2 g: x--->6-3|x|

Each sentence defines a relation and x and y are real numbers. graph relation and tell whether it's a function.

a.{(x,y):y=|1-x|}

b.{(x,y):|y|<=1-|x|}

c.{(x,y):x^2=4y^2

Please help, I really do not understand it. An explanation would be highly appreciated.

Re: ALgebra 2 Function and Relations

Hey xotinalx.

For 2D function, the easiest way to know if something is a function is if you can draw a vertical line anywhere and it only crosses the function once. So as an example the relationship x^2 + y^2 = 1 is not a function unless you restrict it further but y = x^2 is.

Mathematically this means that if y = f(x) then it means that if you have two values where a = f(b) and c = f(d), then something is a function if and only if b = d implies that a = c (or in other words, I give you an x and you can only give me back 1 y).