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

1 Answer
Daniel L.
Oct 8, 2017

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.

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