How do you decide whether the relation $x^{2} - 3 y = 12$ $x^2-3y =12$ defines a function?

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How do you decide whether the relation $x^{2} - 3 y = 12$ $x^2-3y =12$ defines a function?

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Answer 1 · 2015-11-01T12:13:46

A function is when for every $x$ $x$ there is a maximum of only one $y$ $y$

Explanation:

Let's rewrite the relation by adding $3 y$ $3y$ to both sides and subtracting $12$ $12$ (also on both sides) and then divide by $3$ $3$ :

$x^{2} - 3 y = 12 \to x^{2} - 12 = 3 y \to y = \frac{1}{3} x^{2} - 4$ $x^2-3y=12->x^2-12=3y->y=1/3x^2-4$
graph{x^2/3-12 [-28.86, 28.87, -14.43, 14.43]}
This gives one $y$ $y$ -value for every $x$ $x$ , so this may be called $y (x)$ $y(x)$ , or $y$ $y$ as a function of $x$ $x$ .

Note :
You can not write $x (y)$ $x(y)$ , or $x$ $x$ as a function of $y$ $y$ , because for many $y$ $y$ 's there are two possible $x$ $x$ 's.

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How do you decide whether the relation $x^{2} - 3 y = 12$ $x^2-3y =12$ defines a function?

1 Answer

Explanation:

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How do you decide whether the relation x2−3y=12x^2-3y =12 defines a function?

1 Answer

Explanation:

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How do you decide whether the relation $x^{2} - 3 y = 12$ $x^2-3y =12$ defines a function?