Is (-2,1), (-1,2), (1,1), (2,3) a function?

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Is (-2,1), (-1,2), (1,1), (2,3) a function?

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Answer 1 · 2015-07-07T15:09:36

Yes. There is no pair (a,b), (a,c) with $b \neq c$ $b \ne c$ .

Explanation:

You don't need a specific function. But,
choose a model of function with 4 parameters a,b,c,d.
$y = a x^{3} + b x^{2} + c x + d$ $y = ax^3 + bx^2 + cx + d$

$1 = - 8 a + 4 b - 2 c + d$ $1 = -8a + 4b -2c + d$

$2 = - a + b - c + d$ $2 = -a + b - c + d$

$1 = a + b + c + d$ $1 = a + b + c + d$

$3 = 8 a + 4 b + 2 c + d$ $3 = 8a + 4b + 2c + d$

If you solve this matrix, you'll find:

$f (x) = \frac{1}{2} x^{3} - \frac{13}{6} x^{2} - x + \frac{11}{3}$ $f(x) = 1/2x^3 -13/6x^2 - x + 11/3$

$y = \frac{3 x^{3} - 13 x^{2} - 6 x + 22}{6}$ $y = (3 x^3 -13x^2 - 6x + 22)/6$

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Is (-2,1), (-1,2), (1,1), (2,3) a function?

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