Question

Which of the following best describes the equation below?

y= x/3

(a) both a relation and a function

(b) relation only

(c) function only

(d) neither a relation nor a function

Answer 1

(a) both a relation and a function

Explanation:

In math, the relation is between the x-values and y-values of ordered pairs. The set of all x-values is called the domain, and the set of all y-values is called the range. We must have a value of y for a value of x and so it's a relation.

Here , y = x/3 for every value of x we have a value of y as at x=1 we have y=1/3. So, it is a relation. Now, Relation is function when it passes vertical line test i.e. when we draw graph of y if we sketch many distinct vertical lines they all must cut graph at only one point and so its function. Basically, for every value of x we must have only one value of y. Y = x/3 follows the above rule and so its also a function! ∴ y=x/3 is both a relation & a function.