how do you do this?

Question

Does the following set of ordered pairs express the first variable as a function of the second variable?
{(3, 4)(-3, 2)(3, -3)(-3, -4)(1, -1)(-1, -3)}

A. yes
B. no

Answer 1

To keep things simple, I'll refer to the ordered pairs as (x,y). So the basic question is, can these ordered pairs all fit into some equation f(y)=x (in other words, can x be a function of y). If f(y)=x, then a given value of y will lead to a discrete value of x. However, the same y-value appears in two ordered pairs, (3,-3) and (-1,-3). Therefore, x cannot be a function of y. There is no function for which 1 value of the independent variable results in two distinct solutions. There are such equations (x^2 + y^2 = 2), but these cannot be put into the form f(y) = x and are not functions.

Conversely, consider the vertical line test. For a function f(x) = y, if any vertical line crosses the graph at 2 or more points, it is not the graph of a function. Since this question asks about the equation f(y) = x, you would use a horizontal line test. The horizontal line y = -3 would touch the graph at both 3 and -1, so these could not be ordered pairs from any function f(y) = x.

Just as a matter of interest, it could also not be a function f(x) = y because of the points (3,4) and (3,-3).

Answer 2

NO.
(3,4) and (3,-3) indicate that x= 3 has two different values. For there to be a function, there can be only one value of y for each value of x. (-3,2) and (-3,-4) also violate the definition of a function.

y is not a function of x for the above set of ordered pairs.

Answer 3

B. no since there does not appear to be any order in that pairing.

Answer 4

If am so not sure, but I'd guess no

Answer 5

A

Answer 6

B