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

Jul 7, 2015

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

#### Explanation:

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

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

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

$1 = a + b + c + d$

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

If you solve this matrix, you'll find:

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

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