Question

In which choice is y a function of x?

Answer 1

First choice

Explanation:

Check if a relation is a function by looking at the x's.

No repeated x's? Then it's a function.

Repeated x's but the y is the same y both times? It's a function.

Repeated x's and different y's? NOT A FUNCTION.

see image

Answer 2

The set (1, 3), (3, 4), (4, 5), (5, 6) is the only one representing a function, as each x-value corresponds to a unique y-value, meeting the criteria of a mathematical function.

A function is a relation between a set of inputs (domain) and a set of possible outputs (range) such that each input is related to exactly one output. In mathematical terms, if (x, y) is a pair in a function, it means that for a given value of x, there is a unique value of y.

Let's examine each choice:

(1, 3), (3, 4), (4, 5), (5, 6): This set represents a function because each x-value corresponds to a unique y-value.

(2, 0), (2, 3), (4, 5), (6, 7): This set does not represent a function because the x-value 2 is associated with two different y-values (0 and 3).

(2,5), (4, 8), (6, 10), (2, 12): This set does not represent a function because the x-value 2 is associated with two different y-values (5 and 12).

(6, 2), (4, 1), (6, 8), (8, 10): This set does not represent a function because the x-value 6 is associated with two different y-values (2 and 8).

The only choice where y is a function of x is the first one: (1, 3), (3, 4), (4, 5), (5, 6).