Explained: "How to decide whether the relation x2−3y=12 defines..."

Jasmine Young

Answered question

2022-12-28

How to decide whether the relation

x^{2} - 3 y = 12

defines a function?

peannreu

Beginner2022-12-29Added 10 answers

Rewrite the relationship by including

3 y

to both sides and subtracting

12

(also on both sides) and then divide by

3

x^{2} - 3 y = 12 \to x^{2} - 12 = 3 y \to y = \frac{1}{3} x^{2} - 4

graph{x^2/3-12 [-28.86, 28.87, -14.43, 14.43]}
This gives one

y

-value for every

x

, so this may be called

y (x)

, or

y

as a function of

x

.
Note :
You can not write

x (y)

, or

x

as a function of

y

, because for many

y

's there are two possible

x

's.

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