Question

How do you find the domain and range and determine whether the relation is a function given :`y=x^2`?

Answer 1

See explanation.

Explanation:

The domain is the maximum subset of `RR` for which expression can be calculated. Here we do not have any limitations. Any treal number can be raised to the second power, so the domain is `RR`.

Any real number raised to the second power gives a non-negative result (0 or a positive real number), so the range is: `r=[0;+oo)`

To find if a relation is a function we have to check if there are arguments (`x`) with more than one value `y`. You can do it looking at the graph:

graph{(y-x^2)=0 [-10, 10, -5, 5]}

If we have drawn the graph we can check if there is a vertical line crossing the graph in more than one point.

If such point existed, the relation would not be a function. (There would be an argument with more than one value.)

Here there are no such values. So the relation is a function.