Functions, Inverses, and Compositions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What is the inverse of a function?

Back

The inverse of a function is a function that reverses the effect of the original function, meaning if f(x) = y, then f⁻¹(y) = x.

Front

How do you find the inverse of a set of points?

Back

To find the inverse of a set of points, switch the x and y coordinates of each point.

Front

What is function composition?

Back

Function composition is the process of applying one function to the results of another function, denoted as (f ∘ g)(x) = f(g(x)).

Front

What is the composition of f(x) = x + 2 and g(x) = 3x?

Back

(f ∘ g)(x) = f(g(x)) = f(3x) = 3x + 2.

Front

What does it mean for two functions to be inverses?

Back

Two functions are inverses if their composition results in the identity function, meaning f(f⁻¹(x)) = x and f⁻¹(f(x)) = x.

Front

What is the identity function?

Back

The identity function is a function that always returns the same value that was used as its input, denoted as I(x) = x.

Front

How can you tell if a graph represents a function?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once (Vertical Line Test).

Front

What is the Vertical Line Test?

Back

The Vertical Line Test is a method to determine if a curve is a function by checking if any vertical line crosses the curve more than once.

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.