Question

Does the relation |y – 2| = x define y as a function of x?
1) True
2) False

Answer 1

The relation |y - 2| = x does not define y as a function of x because for every value of x, there are two possible values of y.

Step-by-step explanation:

The relation |y - 2| = x does not define y as a function of x. In order for a relation to be a function, each value of x must correspond to a unique value of y. However, in this relation, for every value of x, there are two possible values of y.

For example, when x = 3, the possible values of y can be found by substituting x = 3 into the relation: |y - 2| = 3. This gives two equations: y - 2 = 3 and y - 2 = -3. Solving these equations, we get y = 5 and y = -1. Therefore, for x = 3, we have two values of y: 5 and -1.

Since there are multiple values of y for some values of x, the relation does not define y as a function of x. Therefore, the correct answer is 2) False.