If x and y are intergers, find the domain of {(x,y): |y| = x and x is less than or equal to 4}?

Question

Is it a function?

Answer 1

As a couple of respondents have observed, since x is equal to the absolute value of y, it can't be negative. The only non-negative integers up to 4 are {0, 1, 2, 3, 4}, which is therefore the domain of the relation. Those respondents who referred to this as a relation obviously realised it isn't a function, because y can be equal to either x or -x; e.g. the domain value x = 3 gives y = 3 or -3.

The range (yes, I know you didn't ask for it!) is
{-4, -3, -2, -1, 0, 1, 2, 3, 4}

Answer 2

Domain: 0 < x < 4

Answer 3

{(x,y): |y| = x, and x <= 4, x,y are integers} is a relation between two numbers, x and y.

Thus, domain of the relation is, conventionally, the set of values defined for x. In this case, the set of values defined for x are integers less than or equal to 4, which is {x: x<=4, and x is an integer} = {4,3,2,1,0,-1,-2,-3,...}.

In addition the range of the relation is the absolute values of the domain, which is {4,3,2,1,0,1,2,3,...}
= {0,1,2,3,4,...}
= the set of non-negative integers

Answer 4

you won't be able to easily plug in a answer like x=2 and y=2, see that it extremely works, and then say "There, that proves it." it really is not any longer a proof! 0 <= (x-y)^2, on account that squaring a authentic kind not in any respect factors a adverse. From there: 0 <= x^2 - 2xy + y^2 4xy <= x^2 + 2xy + y^2 4xy <= (x+y)^2 xy <= (x+y)^2 / 4 ?(xy) <= (x+y)/2

Answer 5

x can be:

all negative numbers because they are less than 4

all positive numbers less than 4.

So if you trace the number line for all permitted x you will have all the numbers to the left of 4.

If you take the absolute value of all the numbers described above, you come up with all the positive numbers. (let it sink in for moment through the help of the first item i have given, "all negative numbers because they are less than 4")