Thread: Defining Functions

The following statements each describe a relationship between two sets A and B in which the given elements are in the set A. Identify the sets A and B precisely in each case. Determine whether or not the relationship defines a function f:A->B.

a. The triangle T is circumscribed by the given circle C.
b. The circle C circumscribes the given triangle T.
c. The area of a given triangle T is A.
d. The pair {p,q} of points in the plane are the foci of a given ellipse E.

My answers:
a. A is the set of circles. B is the set of triangles. Function.
b. A is the set of triangles. B is the set of circles. Function.
c. A is the set of triangles. B is the area. Function.
d. A is the set of ellipses. B is the set of points. Not a function.

Originally Posted by lovesmath

a. The triangle T is circumscribed by the given circle C. ...
My answers:
a. A is the set of circles. B is the set of triangles. Function.

So, you think that a given circle circumscribes at most one triangle?

Originally Posted by lovesmath

b. The circle C circumscribes the given triangle T. ...
b. A is the set of triangles. B is the set of circles. Function.

Agree.

Originally Posted by lovesmath

c. The area of a given triangle T is A. ...
c. A is the set of triangles. B is the area. Function.

What a bad practice of confusing the area A with the set A on the part of the problem authors. B should be the set of (nonnegative) real numbers. The area of a triangle is an individual number, it can't qualify for a set B.

Originally Posted by lovesmath

d. The pair {p,q} of points in the plane are the foci of a given ellipse E. ...
d. A is the set of ellipses. B is the set of points. Not a function.

Judging by the curly braces, {p, q} is a set of points and not an ordered pair. B should be a set of sets with at most two elements. Why do you think this is not a function?