If the rule of a relation is y is found by squaring x and then adding 3," is the relation a function?

Yes, it is a function

Explanation:
The relation is obtained by squaring the value of x and then adding 3.
This means that the equation would be:
y = x² + 3

Now, taking a look at this equation, we would find that each value of x would have only one value of y.

Since a function is defined as a relation in which each x-value has only one y-value, therefore, the given equation represents a function.

This can be illustrated more by graphing the given relation (graph is shown in the attached image).
You will find a parabola is formed where each x value has only one corresponding y-value.

Hope this helps :)