Question

Find the domain and range of the relation and determine whether it is a function. y=x2-3

Answer 1

is that supposed to be x squared or 2x

Answer 2

A relation is a set of pairs, like {(2, 1), (5, 9), (3, 7)}

If the first coordinate is not repeated, like in this example, were we have only (2, 1) and not also (2, 8), for instance, then the relation is called a function.


A relation sometimes has too many pairs to be expressed by listing all of them. in such cases we use formulas which describe all the pairs.

We are given the relation is $y=x^2-3$. This means that all pairs of this relation, are such that the second coordinate, is the first one squared, minus 3.

So each pair of this relation is : $(x, x^2-3)$


For any x, $x^2-3$ is only one value, 

for example, if x=10, y can only be $x^2-3=10^2-3=97$


We cannot possibly have both (10, 97) and (10, 16), for example, because the formula does not allow that.

this means 10 does not repeat as a first pair in this relation, and nor does any other value.


this makes the relation a function


The Domain is the set of all possible values x can be. Clearly, x can be any value, because no x makes $x^2-3$ undefined


Answer: The relation is a function, with Domain all real numbers