(Quiz) Basics about Function

Function definition

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Saying y is a function of x means y is related to x by some formula

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Functions can be defined that have nothing to do with numbers

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POINTS (1)

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Ordered Pairs

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An ordered pair (1, 2) = (2, 1)

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Coordinates as ordered pair

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The point (3, 4) is different from the point (4, 3).

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Cartesian Product of Two Sets A and B

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Let A = {1, 2, 3} and B = {5, 6}, what is the cartesian products of these two sets?

A × B = ?

{(1, 5), (2, 5), (3, 5), (1, 6), (2, 6)}

{(1, 5), (2, 5), (3, 5), (1, 6), (3, 6)}

{(1, 5), (2, 5), (3, 5), (2, 6), (3, 6)}

{(1, 5), (2, 5), (3, 5), (1, 6), (2, 6), (3, 6)}

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POINTS (1)

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The cartesian product of A x B = B x A

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Number of elements in the cartesian product set A x B

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Let A = {1, 2, 3, 4}, and B = {5, 6, 7}, Then the number of elements in the cartesian product set A x B =

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POINTS (1)

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Equality of ordered pairs

Two ordered pairs (a, b) and (c, d ) are equal if a = and b =

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POINTS (1)

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Definition of a Function

Let A and B be two nonempty sets.

A function ƒ from A to B is a subset of (1) transparent (involving the entire set (2) ) with the property that each “a” belonging to A, belongs to precisely one ordered pair (a, b), in the subset of A x B, under consideration. In other words, a function ƒ from set A to set B consists of a set of ordered pairs (a, b) A x B such that no two order pairs have the same (3) transparent element.

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A x B

second

first

B x A

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POINTS (1)

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Alternative definition of a "Function"

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A function ƒ from set A to set B (written as ƒ: A → B) is a rule of correspondence that associates to each element of A, one and only one element of B.

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POINTS (1)

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A function from set A to set be is also called a mapping from A to B

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True

False

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POINTS (1)

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We observe the following in a function from set A to set B

Each element of (1) need not be in the association, but every element of (2) must be involved in it.
One element of (3) cannot be associated with more than one element of (4) , but one element of (5) may correspond to two or more elements of (6) .

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POINTS (1)

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Does the following figure represent a function?

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Yes

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POINTS (1)

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Does the following figure represent a function?

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Yes

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POINTS (1)

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Does the following figure represent a function?

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Yes

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POINTS (1)

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Does the following figure represent a function?

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Yes

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POINTS (1)

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Explanation

Does the following figure represent a function?

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Yes

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POINTS (1)

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The (entire) set A is called

Let ƒ be a function from set A to set B ( ƒ: A → B), then

The (entire) set A is called the of ƒ.

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POINTS (1)

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The (entire) set B is called

Let ƒ be a function from set A to set B ( ƒ: A → B), then

The (entire) set B is called the of ƒ.

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POINTS (1)

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An element of B that corresponds to some element x of A

Let ƒ be a function from set A to set B (ƒ: A → B), then

An element of B that corresponds to some element x of A is denoted by ƒ(x), and it is called the of x under ƒ.

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POINTS (1)

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The set of all images

Let ƒ be a function from set A to set B (ƒ: A → B), then

The set of all images constitutes the of ƒ. The of ƒ is denoted by ƒ(A) and it is a of set B. In other words ƒ(A) ⊆ B.

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range

subset

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POINTS (1)

Function definition

Correct Answer

Explanation

Functions can be defined that have nothing to do with numbers

Correct Answer

Explanation

Ordered Pairs

Correct Answer

Explanation

Coordinates as ordered pair

Correct Answer

Explanation

Cartesian Product of Two Sets A and B

Correct Answer

Explanation

The cartesian product of A x B = B x A

Correct Answer

Explanation

Number of elements in the cartesian product set A x B

Correct Answer

Explanation

Equality of ordered pairs

Correct Answer

Explanation

Definition of a Function

Correct Answer

Explanation

Alternative definition of a "Function"

Correct Answer

Explanation

A function from set A to set be is also called a mapping from A to B

Correct Answer

Explanation

We observe the following in a function from set A to set B

Correct Answer

Explanation

Does the following figure represent a function?

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Explanation

Does the following figure represent a function?

Correct Answer

Explanation

Does the following figure represent a function?

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Explanation

Does the following figure represent a function?

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Explanation

Does the following figure represent a function?

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Explanation

The (entire) set A is called

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Explanation

The (entire) set B is called

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Explanation

An element of B that corresponds to some element x of A

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The set of all images

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Explanation

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