Question

Which relation is a function? Select all that apply.

{(5,5), (4,4), (3, 3), (2,2)}


{(5,1), (4,1), (3, 1), (2,1)}


{(5,3), (4,1), (3, 2), (2,0)}


{(5,2), (2,5), (5, 3), (3,5)}


{(5,1), (5,2), (5, 3), (5,4)}

Answer 1

The first 3 are functions as their x coordinate (number on the left side of the parentheses) is not repeated in any of the other parentheses

Answer 2

We need to see which of the given relations are functions, the correct options are:

• A) {(5,5), (4,4), (3, 3), (2,2)}
• B) {(5,1), (4,1), (3, 1), (2,1)}
• C) {(5,3), (4,1), (3, 2), (2,0)}

Let's start by describing what a function is.

A function is a relation that maps elements from one set, the domain, into elements from another set, the range.

Such that the notation used is (x, y). This means that the element x is being mapped into y.

And each element on the domain can be mapped into only one element on the range.

So, to know if the relations are functions or not, we need to see if there are repeated first values in the coordinate pairs. If that is the case, then the relation does not represent a function.

So we have:

A) {(5,5), (4,4), (3, 3), (2,2)}

represents a function.

B) {(5,1), (4,1), (3, 1), (2,1)}

represents a function.

C) {(5,3), (4,1), (3, 2), (2,0)}

represents a function.

D) {(5,2), (2,5), (5, 3), (3,5)}

Does not represent a function, because x = 5 is being mapped into two different values.

E) {(5,1), (5,2), (5, 3), (5,4)}

Does not represent a function, because x = 5 is being mapped into two different values.

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