Functions Flashcard

Front

Function

Back

A relation that associates every element of A with one and only one element of B

Answer explanation

A function is defined as a relation that associates every element of A (the domain) with one and only one element of B (the codomain). This ensures that each input has a unique output, making the correct choice the third option.

Front

What is the domain of a function?

Back

The set of all possible inputs

Answer explanation

The domain of a function refers to the set of all possible inputs that can be used in the function. This is why 'The set of all possible inputs' is the correct answer, as it defines the values that can be fed into the function.

Front

Injective function

Back

A function where every element of B is the image of at most one element of A

Answer explanation

An injective function maps each element of set A to a unique element in set B, meaning no two elements in A share the same image in B. Thus, every element of B is the image of at most one element of A.

Front

What does it mean for a function to be surjective?

Back

Every element of B is the image of at least one element of A

Answer explanation

A function is surjective if every element of the codomain (set B) is the image of at least one element from the domain (set A). This means that all elements in B are covered by the mapping from A.

Front

What is a biunivocal function?

Back

A function that is both injective and surjective

Answer explanation

A biunivocal function is defined as a function that is both injective (one-to-one) and surjective (onto), meaning every element in set A maps to a unique element in set B, and all elements in B are covered.

Front

What does the horizontal line test determine?

Back

If a function is injective

Answer explanation

The horizontal line test determines if a function is injective (one-to-one). If any horizontal line intersects the graph of the function more than once, the function is not injective.

Front

Periodic function

Back

A function that repeats its values at regular intervals

Answer explanation

A periodic function is defined as one that repeats its values at regular intervals. This means that for some period T, the function f(x) satisfies f(x) = f(x + T) for all x, making the second choice the correct answer.

Front

What is the natural domain of a function?

Back

The largest set of real values for which the function is defined

Answer explanation

The natural domain of a function is the largest set of real values for which the function is defined, meaning it includes all inputs that produce valid outputs. This makes the correct choice the largest set of real values.

Front

What is the graphical representation of a function?

Back

A set of points in the Cartesian plane

Answer explanation

The graphical representation of a function is a set of points in the Cartesian plane, where each point corresponds to an input-output pair of the function. This choice accurately describes how functions are visualized.

Front

Condition for a function to be increasing?

Back

f(x1) < f(x2) for all x1 < x2

Answer explanation

A function is increasing if for any two points x1 and x2, where x1 < x2, the function value at x1 is less than the function value at x2. Thus, the correct condition is f(x1) < f(x2) for all x1 < x2.