PLZZZ HELP DUE IN 5 MINS Which set of ordered pairs represents a function?

{(2, 9), (5, 9), (1, -6), (-5, 5), (2,9), (5,9), (1,−6), (−5,5)}
{(6, 6), (6, 8), (-8, -7), (-3, -8), (6,6),(6,8),(−8,−7),(−3,−8)}
{(1, 8), (9, -3), (7, -4), (7, -6), (1,8),(9,−3),(7,−4),(7,−6)}
{(-5, -1), (-3, -7), (-5, 3), (-7, -4), (−5,−1),(−3,−7),(−5,3),(−7,−4)}

{(2, 9), (5, 9), (1, -6), (-5, 5), (2,9), (5,9), (1,−6), (−5,5)}

Step-by-step explanation:

recall that for a function to be valid, every input must give one and only 1 output. (i.e every x-ordinate must have only one unique corresponding y-ordinate)

I have highlighted in bold and underlined the entries for each of the other choices where an x-value gives more than one possible y-value, hence these are not functions. only the first option satisfies this condition:

{(2, 9), (5, 9), (1, -6), (-5, 5), (2,9), (5,9), (1,−6), (−5,5)} Every x-value has a unique y-value, so it is possible that this is a function.

{(6, 6), (6, 8), (-8, -7), (-3, -8), (6,6),(6,8),(−8,−7),(−3,−8)}  (not a function)

{(1, 8), (9, -3), (7, -4), (7, -6), (1,8),(9,−3),(7,−4),(7,−6)} (not a function)

{(-5, -1), (-3, -7), (-5, 3), (-7, -4), (−5,−1),(−3,−7),(−5,3),(−7,−4)} (not a function)

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: