Question

Consider the Equation y > 3x + 1 (a) Find an ordered pair that satifies the equation (b) Is the equation a Releation? explain (c) Is the equation a Function? explain

Answer 1

(a) (1,5)

(b) Every subset of a cartesian product is a relation, therefore this is a relation.

(c) The relation IS NOT a function.

Explanation:

(a)

(1,5)

Notice that 3(1) +1 = 4 < 5 therefore (1,5) is an order pair that satisfies the equation.

(b)

Every subset of a cartesian product is a relation, therefore this is a relation.

(b)

A relation is a function of the following condition holds

if (a,b) and (c,b) belong to the relation then (a=c)

In this case, (1,5), (0,5) belong to the relation but 0 is different than 5, therefore the relation IS NOT a function.