Functions Quiz

What is the definition of a function?

• A relation that has no restrictions on the elements of A and B

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

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

• A relation that associates every element of A with multiple elements 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.

What is the domain of a function?

• The set of all images of elements in B

• The set of all possible outputs

• The set of all elements in A and B

• 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.

What is an injective function?

• A function that has no images

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

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

• A function that is both injective and surjective

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.

What does it mean for a function to be surjective?

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

• No element of B is an image of any element of A

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

• Every element of A is mapped to multiple elements of B

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.

What is a biunivocal function?

• A function that is both injective and surjective

• A function that maps every element of A to multiple elements of B

• A function that is neither injective nor surjective

• A function that has no images

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.

What does the horizontal line test determine?

• If a function is surjective

• If a function is even

• If a function is injective

• If a function is periodic

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.

What is the definition of a periodic function?

• A function that is always increasing

• A function that repeats its values at regular intervals

• A function that has no defined period

• A function that is only defined for positive values

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.

What is the natural domain of a function?

• The set of all integers

• The set of all real numbers

• The set of all outputs of the function

• 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.

What is the graphical representation of a function?

• A random set of points

• A single line in the Cartesian plane

• A set of points in the Cartesian plane

• A collection of curves that do not intersect

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.

What is the condition for a function to be increasing?

• f(x1) > f(x2) for all x1 < x2

• f(x1) = f(x2) for all x1 < x2

• f(x1) < f(x2) for all x1 < x2

• 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.