Final answer:
The equation x² - 7y = 3 indeed defines y as a function of x because after rearranging it to y = (x² - 3) / 7, each x corresponds to exactly one y value.
Step-by-step explanation:
To determine if the equation x² - 7y = 3 defines y as a function of x, we must be able to express y explicitly in terms of x and for each value of x there should be exactly one corresponding value of y. Rearranging the equation to solve for y, we get:
y = (x² - 3) / 7
Now, for any given value of x, there is only one possible value for y. Therefore, y is a function of x. In contrast, if rearranging resulted in an equation where a single x value corresponded to multiple y values, y would not be a function of x. As the equation is a quadratic polynomial divided by a constant, it suggests that every x value will produce a unique y value, following the definition of a function.