Decide whether the relation defines $y$ as a function of $x$ and give the domain and range. \[ y=x^{2} \] Does the relation define a function? No Yes What is the domain? (Type your answer in interval notation.)

Step 1 ：The given relation is \(y=x^{2}\). This is a standard form of a quadratic function. In this function, for each value of \(x\), there is exactly one corresponding value of \(y\). Therefore, this relation defines \(y\) as a function of \(x\).

Step 2 ：The domain of a function is the set of all possible input values (in this case, \(x\) values) which will produce a valid output. Since \(x\) can be any real number and we can square any real number, the domain of this function is all real numbers.

Step 3 ：The range of a function is the set of all possible output values (in this case, \(y\) values). Since squaring any real number gives a non-negative result, the range of this function is all non-negative real numbers.

Step 4 ：Final Answer: The relation does define \(y\) as a function of \(x\). The domain is all real numbers, which in interval notation is \((-\infty, \infty)\). The range is all non-negative real numbers, which in interval notation is \([0, \infty)\).