Final Answer:
A) The relation y = x² represent y as a function of x. Thus, the correct answer is option a) Yes, the relation represents a function.
B) The relation x² + y² = 25 does not represent y as a function of x. Thus, the correct answer is option b) No, the relation does not represent a function.
Step-by-step explanation:
A) The relation y = x² represents a function because for each x value, there is a unique corresponding y value. In other words, every input x has only one output y, satisfying the definition of a function. This can be visually confirmed by the fact that if you draw the graph of y = x², it passes the vertical line test, meaning that no vertical line intersects the graph more than once.Therefore, the correct answer is option a) Yes, the relation represents a function.
B) The relation x² + y² = 25 does not represent y as a function of x. To see why, consider that for certain x values, there are two possible y values that satisfy the equation. For example, when x = 3, we have y = 4 and y = -4, both satisfying the equation. This violates the definition of a function, which requires that each input has only one corresponding output. Therefore, the correct answer is option b) No, the relation does not represent a function.