Question

Which of the following lists of ordered pairs is a function?

Answer 1

D

Explanation:

Note that a relation is not a function if any input (i.e. element of domain) is mapped to more than one output (i.e. element of range).

In relation A, the input x=2 is mapped to both y=3 and y=5. So, the relation A is not a function.

In relation B, the input x=2 is mapped to both y=5 and y=1. So, the relation B is not a function.

In relation C, the input x=4 is mapped to both y=0 and y=3. So, the relation C is not a function.

In relation D, every input is mapped to a unique output. So, the relation D is a function.

Answer 2

D. (2, 5), (3, 6), (6, 9)

Explanation:

In order for y = f(x) to be a function, each value of x can correspond to only one value of y.

Therefore, the correct option should not have two or more ordered pairs with the same x value but different y values.

For example, let's look at option A:

(-1, 2), (2, 3), (3, 1), (2, 5).

We can see that the second and fourth pairs, (2, 3) and (2, 5), both have 2 as their x-value, but their y-values are different. This means that the function gives different values of f(x) for the same value of x, and therefore it cannot be a function.

Similarly, in options B and C, we see pairs with the same values of x but different values of y. Therefore options B and C are also incorrect.

In option D, there are no pairs where the same x-value corresponds to different y-values, so D is the correct option.