Question

(don't understand but I think its easy)Which of the following relations is a function?

A. {(-3, -1), (-1, -3), (-3, -3), (9, 4), (2, 3)}
B. {(1, 7), (2, 8), (4, 5), (0, 0), (3, 5)}
C. {(2, 5), (5, 6), (2, 3), (1, 7), (0, 2)}
D. {(6, 1), (5, 8), (9, 9), (5, 9), (5, -3)}

Answer 1

The correct answer option is B. {(1, 7), (2, 8), (4, 5), (0, 0), (3, 5)}.

Explanation:

We are to determine whether which of the given relations in the possible answer options is a function.

We know that the x values of a function cannot be repeated. It means that for each output, there must be exactly one input.

Therefore, we will look for the relation where no x value is repeated.

Function ---> {(1, 7), (2, 8), (4, 5), (0, 0), (3, 5)}

Answer 2

B. {(1, 7), (2, 8), (4, 5), (0, 0), (3, 5)}

Explanation:

You are right, it is easy. Any relation with a repeated first value is not a function.

A has (-3, -1) and (-3, -3), so the value -3 is a repeated first value.

C has (2, 5) and (2, 3), so the value 2 is a repeated first value.

D has (5, 8), (5, 9), and (5, -3), so the value 5 is a repeated first value.

None of A, C, or D is a relation that is a function. The correct choice is B, which has first values 0, 1, 2, 3, 4 -- none of which is repeated.

_____

If you plot points with repeated first values, you find they lie on the same vertical line. If a vertical line passes through 2 or more points in the relation, that relation is not a function. We say, "it doesn't pass the vertical line test."

A relation must pass the vertical line test in order to be a function. This is true of graphs of any kind, not just graphs of discrete points.