Question

Which of the following relations shows a function?

a) {(5, -7), (6, -7), (-8, -1), (0, -1)}
b) {(4, -1), (4, -2), (3, -1), (2, 4)}
c) {(4, 5), (3, -2), (-2, 5), (4, 7)}
d) {(1, 4), (4, 1), (1, -4), (-4, 1)}

Answer 1

A function cannot use the same number twice as an x-coordinate.
Look at each choice.
If you see the same x-coordinate used more than once, it is not a function.
If each x-coordinate is used only once, it is a function.

Answer 2

i chose C as my answer, would i be correct?

Answer 3

Examples:

{(0, 1), (2, 5), (4, 6), (7, 5)} is a function since the x-coordinates are all different. 0, 2, 4, 7 are all different x-coordinates.

{(0, 5), (6, 8), (0, 4), (5, 10)} is not a function because 0 is used twice as an x-coordinate.

Answer 4

Look at C in your problem. What are the x-coordinates?
Please list them.

Answer 5

oh sorry i see that 4 is in two x coordinates

Answer 6

Correct.
That shows you C is not a function.

Answer 7

so would it be A?

Answer 8

a) \(\{(\color{red}{5} , -7), (\color{red}{6}, -7), (\color{red}{-8}, -1), (\color{red}{0}, -1)\} \)
b) \(\{(4, -1), (4, -2), (3, -1), (2, 4)\} \)
c) \(\{(4, 5), (3, -2), (-2, 5), (4, 7)\} \)
d) \(\{(1, 4), (4, 1), (1, -4), (-4, 1)\}\)

Answer 9

Correct.
It's the only choice in which every x-coordinate is a different number.

Answer 10

okay thank you!

Answer 11

Definition of Function:
A relation in which no two ordered pairs have the same x-coordinate.

Answer 12

You're welcome.