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y² = x

--> y = ±√x

Because there are *two* square roots for any positive number (positive and negative) this will not be a function.

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Q: Give an example of a relation that is NOT a function and explain why it is not a function?
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What are function and relation?

A function is an equation that gives a unique answer. A relation does not. Example: y = 3x + 1 is a function. If I give you x, you can determine y. And that y is unique to that x. So if x = 1, you know y = 4. No other of x gives y = 4 as an answer. So y = 3x + 1 is a function. Example: y = 4x2. So if I give you x = 1, y = 4. But y = 4 if I also give you x = -1. So y = 4x2 is not a function, it is a relation.


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The idea of a function is that when you give it an input number, it will always give you a unique output number. Examples: y = 2x (y is a function of x) h = 1/x2 + 5 (h is a function of x) z = 23 + 3y - x + x/y (z is a function of x and y) An equation simply tells you that two things are equal (left side is equal to the right side). Examples: y = 2x (note: also a function) 2x2 + 5 = 50 (not a function, but can be manipulated to become one: [x = squareroot of (50 - 5)/2]) 2 + 19 = 21 (not a function) All functions are equations, but not all equations are functions. Any equation where you have 1 input but more than 1 output is a relation. A function can have different inputs that give the same output, but not 1 input and multiple outputs (example: If you put 5 and -5 as inputs into the function y = x2, you will get the same output of 25.)

Related questions

What are function and relation?

A function is an equation that gives a unique answer. A relation does not. Example: y = 3x + 1 is a function. If I give you x, you can determine y. And that y is unique to that x. So if x = 1, you know y = 4. No other of x gives y = 4 as an answer. So y = 3x + 1 is a function. Example: y = 4x2. So if I give you x = 1, y = 4. But y = 4 if I also give you x = -1. So y = 4x2 is not a function, it is a relation.


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