Expert: Paul Klarreich - 10/14/2008

Question
Hello Can you help me determine the function rule for this set of ordered pairs?
-4,2   -2,1  0,0  1,2
thank you so much

Answer
Questioner:   carmen
Category:  Advanced Math
Private:  No
 
Subject:  high school algebra I (functions)
Question:  Hello Can you help me determine the function rule for this set of ordered pairs?
-4,2   -2,1  0,0  1,2
thank you so much
.............................
Hi, Carmen,

Sorry, but given a finite set of ordered pairs (four in your case), there are an infinite number of possibilities.  ARE YOU SURE you did not leave out some stuff, such as the exact conditions of the problem, and what you are studying (exactly what).

BTW, ordered pairs should be written:  (-4,2),  (-2,1),  (0,0),  (1,2)

If you are restricted to polynomial functions, then, since:

2 points determine a linear (degree 1) polynomial.
3 points determine a quadratic (degree 2) polynomial.
4 points determine a cubic (degree 3) polynomial.

and you have 4 points, you would ASSUME the polynomial has the form:

y = P(x) = ax^3 + bx^2 + cx + d.

Then you would substitute each pair, like this:

2 = P(-4) = a(-4)^3 + b(-4)^2 + c(-4) + d.

You would get four equations in four variables, which you then solve.

Good luck.