Question

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

Answer 1

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}`

Explanation:

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`