Question

Which relation describes a function?

A) {(0, 0), (0, 2), (2, 0), (2, 2)}
B) {(−2, −3), (−3, −2), (2, 3), (3, 2)}
C) {(2, −1), (2, 1), (3, −1), (3, 1)}
D) {(2, 2), (2, 3), (3, 2), (3, 3)}

Explaine Why you chose your answer.

Answer 1

B) {(−2, −3), (−3, −2), (2, 3), (3, 2)}

Explanation:

For a function to be valid, each value within the domain of the function must give exactly one value in the range of the function.

That is to say, for a function to be valid, every value of x must give only 1 unique value for y.

So basically if you have one value of x which gives a value for y, and if the same value for x gives you another value of y which is different than the first time, then you do NOT have a function.

With this in mind, we can see that for option B, every unique value for x, gives an equally unique value for y. Hence this is a function.

Lets compare this with option A (for example)

For A, we can see that for (0,0), an input of x=0, gave y=0. But then notice that the next set of coordinates (0,2), an input of x=0 gave y=2!!!! (this contradicts the first set (0,0), hence this is not a function.

you'll see similar contradictions for

option C (2,-1) vs (2,1)

option D (2,2) vs (2,3)

Answer 2

B) {(−2, −3), (−3, −2), (2, 3), (3, 2)}

Explanation:

For a relation to be a function, every x value must have only one y value. For a, c, and d, some of the x values have multiple different y values