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#