Operations on Functions and Graphs

Flashcards covering the key concepts of operations on functions, graphing functions, and function types.

Operation on Functions

Refers to the mathematical computations that can be performed between two functions, such as addition, subtraction, multiplication, and division.

Sum of Functions

Given two functions f and g, the sum is defined as (f + g)(x) = f(x) + g(x).

Difference of Functions

Given two functions f and g, the difference is defined as (f - g)(x) = f(x) - g(x).

Product of Functions

Given two functions f and g, the product is defined as (f·g)(x) = f(x)·g(x).

Quotient of Functions

Given two functions f and g, the quotient is defined as (f/g)(x) = f(x)/g(x) where g(x) ≠ 0.

Domain of a Function

The set of all permissible input values (x-values) that a function can accept.

Composition of Functions

The composite function of f and g, denoted as (f o g)(x) = f(g(x)).

Vertical Line Test

A method to determine if a curve is a function by checking if any vertical line intersects the graph at more than one point.

Polynomial Function

A function expressed as a polynomial, generally in the form f(x) = a_nx^n + a_{n-1}x^{n-1} + … + a_1x + a_0 where a_n, …, a_0 are real coefficients.

Quadratic Function

A polynomial function of degree 2, generally in the form f(x) = Ax^2 + Bx + C, representing a parabola.