Relations and Functions

Define a relation in mathematics.

• A relation in mathematics is a geometric shape.

• A relation in mathematics is a single number.

• A relation in mathematics is a set of ordered pairs.

• A relation in mathematics is a set of unordered pairs.

What is the domain of a function?

• Set of all irrational numbers

• Set of all real numbers or a subset of real numbers

• Set of all complex numbers

• Set of all integers

Explain the difference between a function and a relation.

• A function and a relation are the same concept.

• A function can map one input to multiple outputs, whereas a relation maps each input to exactly one output.

• A function maps each input to exactly one output, whereas a relation can map one input to multiple outputs.

• A function always has a linear relationship, while a relation can be non-linear.

What is the range of a function?

• Sum of all input values

• Product of all output values

• Set of all possible output values (y-values)

• Average of all output values

Give an example of a function that is not a relation.

• A function where the domain is not defined.

• A function where one output is related to multiple inputs.

• A function where the range is not defined.

• A function where one input is related to multiple outputs.

Discuss the concept of a one-to-one function.

• A one-to-one function is a function where each element in the domain maps to the same element in the codomain.

• A one-to-one function is a function where each element in the domain maps to a unique element in the codomain.

• A one-to-one function is a function where each element in the domain maps to no elements in the codomain.

• A one-to-one function is a function where each element in the domain maps to multiple elements in the codomain.

How can you determine if a relation is a function?

• Check if each input value maps to exactly one output value.

• Check if the relation is reflexive

• Verify if the relation is symmetric

• Count the number of input values

Define the term 'mapping' in relation to functions.

• Mapping in relation to functions is the process of associating each element in the domain with exactly one element in the codomain.

• Mapping is the process of associating multiple elements in the domain with one element in the codomain.

• Mapping involves connecting elements in the codomain to the domain.

• Mapping ensures that each element in the codomain has a unique element in the domain.

What is the difference between an injective and a surjective function?

• An injective function maps every element in the domain to the same element in the codomain

• A surjective function ensures that each input has multiple possible outputs

• The difference between an injective and a surjective function is that an injective function ensures each input has a unique output (one-to-one), while a surjective function guarantees that every element in the codomain is mapped to by at least one element in the domain (onto).

• An injective function guarantees that the function is continuous

Explain the concept of a composite function.

• A composite function is a function that has no input parameters.

• A composite function is a function that results from applying one function to the output of another function.

• A composite function is a function that results from applying a function to itself.

• A composite function is a function that combines two functions into one.