Functions and Their Properties

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 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 does it mean for a function to be one-to-one?

Back

A function is one-to-one if it never assigns the same value to two different domain elements.

Front

What is the inverse of a function?

Back

The inverse of a function f(x) is a function f^-1(x) that reverses the effect of f, such that f(f^-1(x)) = x.

Front

How do you find the inverse of a function graphically?

Back

To find the inverse of a function graphically, reflect the graph of the function over the line y = x.

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 a polynomial function?

Back

A polynomial function is a function that can be expressed in the form f(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_1x + a_0, where a_n, a_(n-1), ..., a_0 are constants.

Front

What is the difference between even and odd functions?

Back

An even function satisfies f(-x) = f(x) for all x, while an odd function satisfies f(-x) = -f(x) for all x.

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the ratio of two polynomials, f(x) = P(x)/Q(x), where Q(x) ≠ 0.