Final answer:
The relation y=x^2-7 defines y as a function of x is True, as it meets the criterion of a function by giving a single output of y for every input of x, represented by a parabola on the graph.
Step-by-step explanation:
The relation y=x^2-7 defines y as a function of x is True.
A function, by definition, gives a single output for each input. That is, for every value of the independent variable x, there is only one value of the dependent variable y. The given relation, y = x2 - 7, meets this criterion because for each value of x, there is a unique corresponding value of y determined by squaring x and subtracting 7.
Given the properties of a quadratic function, which this is, we know that the graph of this function would be a parabola opening upwards. It would not violate the vertical line test, which means that a vertical line would not intersect the graph at more than one point, further confirming that the relation is indeed a function.