Thread: Defining functions.... True or False

Answer true of false to the following questions:

1. It is possible to uniquely define a quadratic function given 4 distinct points.

2. It is possible to uniquely define a constant function given 4 distinct points.

3. It is possible to uniquely define a quartic function given 4 distinct points.

4. It is possible to uniquely define a cubic function given 4 distinct points.

5. It is possible to uniquely define a quintic function given 4 distinct points.

Originally Posted by trae

Answer true of false to the following questions:

1. It is possible to uniquely define a quadratic function given 4 distinct points.

2. It is possible to uniquely define a constant function given 4 distinct points.

3. It is possible to uniquely define a quartic function given 4 distinct points.

4. It is possible to uniquely define a cubic function given 4 distinct points.

5. It is possible to uniquely define a quintic function given 4 distinct points.

The answer would be TRUE to all if you are asking if it is possible for at least one set of 4 distinct points.

However, if you are asking if it is always possible to define a function such functions:

1,2,3,5 are all false, but 4 is true .
Think of the general polynomial equation and the number of constants you have to solve for

isnt 2 true?

Originally Posted by finch41

isnt 2 true?

"Is it always possible to uniquely define a constant function given 4 distinct points"?
No. Because 1 point fixes the constant function.

Thanks...