How do you write the equation in function notation {(-3, -5) (-2, -3) (0, 1)}?

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Answer 1 · 2015-06-21T22:45:01

These three points are colinear and not vertical, so they can be written as a linear function: $f(x) = 2x+1$

If required, restrict the domain to ${-3, -2, 0}$ and the range to ${-5, -3, 1}$

If a line passes through two points $(x_1, y_1)$ and $(x_2, y_2)$ then the slope $m$ of the line is given by the formula:

$m = (Delta y) / (Delta x) = (y_2 - y_1) / (x_2 - x_1)$

In the case of points $(-3, -5)$ and $(-2, -3)$ we have

$m = (-3 - (-5)) / (-2 - (-3)) = 2 / 1 = 2$

In the case of points $(-2, -3)$ and $(0, 1)$ we have

$m = (1 - (-3)) / (0 - (-2)) = 4 / 2 = 2$

So these points lie along a line of slope $2$ with equation:

$f(x) = 2x + c$ for some constant $c$

Since $(0, 1)$ lies on the line $f(0) = 1$

But $f(0) = 2*0 + c = 0 + c = c$

So $c = 1$ and the formula for $f(x)$ is $f(x) = 2x+1$