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

1 Answer
Jun 21, 2015

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

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

Explanation:

If a line passes through two points (x_1, y_1)(x1,y1) and (x_2, y_2)(x2,y2) then the slope mm 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