Defining functions.... True or False

• May 2nd 2008, 07:31 AM
trae
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.
• May 2nd 2008, 07:42 AM
Isomorphism
Quote:

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 :)
• May 3rd 2008, 02:12 PM
finch41
isnt 2 true?
• May 3rd 2008, 09:13 PM
Isomorphism
Quote:

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.
• May 5th 2008, 02:22 PM
trae
Thanks...