Question

Which relation is not a function?

Answer 1

Answer: Choice D

$y = \pm\sqrt{x}$

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Explanation:

The plus/minus indicates we have two equations, and they are

$y = \sqrt{x} \text{ or } y = -\sqrt{x}$

If x is say x = 4, then y is both y = 2 and y = -2 at the same time.

A function is where any x input leads to exactly one and only one y output (assuming the x value is in the domain). Graphing out choice D shows that it fails the vertical line test. This is where a vertical line crosses through more than one point on the graph. For the other answer choices, it is impossible to draw a vertical line through more than one point on the graph, which visually shows they are functions.