ANSWER: TRUE

(1, 1) (2,4) (3,9) (4, 16) (5, 25), ...

In a function, no first element is repeated. Therefore, the given relation is a function.

(1, 1) (2,4) (3,9) (4, 16) (5, 25), ...

In a function, no first element is repeated. Therefore, the given relation is a function.

False because it is a many-to-one function.

Example:

16 can be a square of both 4 and -4.

ANSWER: False

A one to one function is a relation whose first element x is paired with a distinct (not repeated) seecond element y.

In the given statement a real number is paired to its square, the second element is repeated because it does not limit the real number to positive integers or natural numbers. Hence, we can include the negative integers.

Proof:

A real number to its square:

1² = 1 ⇒ (-1)² = 1

2² = 4 ⇒ (-2)² = 4

3² = 9 ⇒ (-3)² = 9

4² = 16 ⇒ (-4)² = 16

The ordered pairs:

(1,1), (2,4), (3,9), (4,16), ...

(-1, 1), (-2, 4), (-3, 9), (-4, 16) ...

We can conclude here that while the first elements x are not repeated, the second elements y (1, 4, 9, 16, ...) are repeated.

This function is a "many to one" relation, where more than one elements of x is paired to a single element of y.

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