Question

Which of the following table represents a function

x 4 4 9 9
y 2 -2 3 -3
x 2 -2 3 -3
y 4 4 9 -9
x 1 -1 1 -1
y 4 5 6 7
x 5 5 6 6
y 1 2 3 4​

Answer 1

x 2 -2 3 -3

y 4 4 9 -9

Explanation:

X has no repeating value so therefore it is a function :). That basically means it does not intersect itself at all.

Answer 2

X [2, -2, 3, -3]

Y [4, 4, 9, -9]

Explanation:

The second choice represents a function.

Remember that a function is defined as a relation that associates to every element of the domain set (X) exactly one element of the range set (Y).

So, you can see that the second option is the only one that fits with the definition of a function, in fact, that can be a quadratic function, because each image is the square power of the domain.

On the other hand, other options violate the defintion of a function, there are just relations, for example, the firsts one assigns to x = 4, two images 2 and -2. Similarly, third and fourth choice do the same.

Therefore, the right answer is the second choice.