Final answer:
Only the value 5 for x makes the relation A a function, as it does not duplicate an existing input value. The relation thus fulfills the definition of a function, with a unique output for each input demonstrating the dependence of y on x.
Step-by-step explanation:
To determine which value of x will make the relation A a function, we must ensure that each input (x-value) maps to exactly one output (y-value). The relation A = {(3,5), (4,9), (7,2), (x,6)} already contains the input values 3, 4, and 7. To maintain the definition of a function, x cannot repeat these numbers.
The potential values for x are 7, 4, 3, and 5. Among these, 5 is the only value not already used as an input. Therefore, if x = 5, the relation A would indeed be a function since every x-value would have a unique y-value, fulfilling the dependence of y on x.
Examples of functions can be represented through a table of points, such as (1,5), (2,10), (3,7), and (4,14), which can be plotted on a graph showing the dependence of y on x. Additionally, linear equations like 7y = 6x + 8, 4y = 8, and y + 7 = 3x all represent functions.