Which of the following relationships is function ?

a. y^2=2x^2

b. domain range
13 0
2 4
-1

c. domain range
3 2
4 1
7

d. y^2=x^2-3x+4

need

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Explanation:

Anything with a y^2 in it is immediately ruled out due to the fact that something like y^2 = x solves to y = x or y = -x. Or in shorthand you would write . The "plus or minus" means we have two equations squished into one, so to speak. So it is possible for an x input to lead to more than one output here. The same applies to choice A and choice D, which we can cross off the list.

We can also cross off choice C for the same reason. The x = 3 input leads to outputs y = 2 and y = 7 at the same time.

A function is only possible if every x input leads to exactly one y output, assuming the x input is defined in the domain of course. Only choice B satisfies this requirement. Each x input (13, 2, and -1) leads to exactly one y output.