Relations and Functions

Front

What is a relation in mathematics?

Back

A relation is a set of ordered pairs, where each pair consists of an input (or domain) and an output (or range).

Front

What defines a function?

Back

A function is a special type of relation where each input is associated with exactly one output.

Front

How can you determine if a relation is a function?

Back

A relation is a function if no input value corresponds to more than one output value.

Front

What is an ordered pair?

Back

An ordered pair is a pair of elements (x, y) where 'x' is the first element (input) and 'y' is the second element (output).

Front

What does it mean for a relation to not be a function?

Back

A relation is not a function if at least one input is associated with multiple outputs.

Front

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, as long as each input has only one output.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) that the function can accept.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What is a vertical line test?

Back

The vertical line test is a method used to determine if a relation is a function by checking if any vertical line intersects the graph of the relation at more than one point.

Front

What are some examples of functions?

Back

Examples of functions include linear functions (y = mx + b), quadratic functions (y = ax^2 + bx + c), and exponential functions (y = a * b^x).