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Math Help - Defining Functions

  1. #1
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    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.
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  2. #2
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    Re: Defining Functions

    Quote Originally Posted by lovesmath View Post
    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?

    Quote Originally Posted by lovesmath View Post
    b. The circle C circumscribes the given triangle T. ...
    b. A is the set of triangles. B is the set of circles. Function.
    Agree.

    Quote Originally Posted by lovesmath View Post
    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.

    Quote Originally Posted by lovesmath View Post
    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?
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