Functions, Functions, Functions

Front

What is a function in mathematics?

Back

A function is a relation where every input (x-value) has exactly one output (y-value).

Front

How can you determine if a relation is a function?

Back

A relation is a function if no x-value is paired with more than one y-value.

Front

What does it mean for a function to be linear?

Back

A linear function is a function that graphs to a straight line, indicating a constant rate of change.

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions have a constant rate of change and graph as straight lines, while nonlinear functions do not have a constant rate of change and can graph as curves.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a relation is a function; if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

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 one-to-one function?

Back

A one-to-one function is a function where each output value is paired with exactly one input value, meaning no two different inputs produce the same output.

Front

What is a composite function?

Back

A composite function is formed when one function is applied to the results of another function, denoted as (f ∘ g)(x) = f(g(x)).

Front

What is an inverse function?

Back

An inverse function reverses the effect of the original function, such that if f(x) = y, then f^(-1)(y) = x.