relation

(noun)

A relation is a connection between numbers in one set and numbers in another.

Related Terms

  • output
  • linear function
  • variable
  • function

(noun)

A collection of ordered pairs.

Related Terms

  • output
  • linear function
  • variable
  • function

Examples of relation in the following topics:

  • Equations and Inequalities

    • An equation states that two expressions are equal, while an inequality relates two different values.
    • An inequality is a relation that holds between two values when they are different.
    • These relations are known as strict inequalities.
    • To compare the size of the values, there are two types of relations:
    • In contrast to strict inequalities, there are two types of inequality relations that are not strict:
  • Symmetry of Functions

    • It is an equivalence relation.
    • Functions and relations can be symmetric about a point, a line, or an axis.  
    • To determine if a relation has symmetry, graph the relation or function and see if the original curve is a reflection of itself over a point, line, or axis.  
    • Determine whether or not a given relation shows some form of symmetry
  • Functions and Their Notation

    • In mathematics, a function is a relation between a set of inputs and a set of permissible outputs.
    • Functions have the property that each input is related to exactly one output.
    • Functions can also be thought of as a subset of relations.
    • A relation is a connection between values in one set and values in another.
    • All functions are relations, but not all relations are functions.
  • Scientific Applications of Quadratic Functions

    • The Pythagorean Theorem is used to relate the three sides of right triangles.
    • Consider the equation relating gravitational force ($F$) between two objects to the masses of each object ($m_1$ and $m_2$) and the distance between them ($r$):
    • The formula relates height ($h$) to initial velocity ($v_0$) and gravitational acceleration ($g$):
    • The equation relating electrostatic force ($F$) between two particles, the particles' respective charges ($q_1$ and $q_2$), and the distance between them ($r$) is very similar to the aforementioned formula for gravitational force:
  • How Trigonometric Functions Work

    • The trigonometric functions are equal to ratios that relate certain side lengths of a  right triangle.  
    • The ratio that relates those two sides is the sine function.
    • The ratio that relates these two sides is the cosine function.
    • The sides of a right triangle in relation to angle $t$.
  • Introduction to Inequalities

    • A strict inequality is a relation that holds between two values when they are different.
    • To compare the size of the values, there are two types of relations:
    • The above relations can be demonstrated in a number line.
    • The following represents the relation $a$ is less than $b$:
    • In contrast to strict inequalities, there are two types of inequality relations that are not strict:
  • Right Triangles and the Pythagorean Theorem

    • The relation between the sides and angles of a right triangle is the basis for trigonometry.
    • The Pythagorean Theorem, also known as Pythagoras' Theorem, is a fundamental relation in Euclidean geometry.
    • The theorem can be written as an equation relating the lengths of the sides $a$, $b$ and $c$, often called the "Pythagorean equation":[1]
  • What is a Linear Function?

    • Vertical lines are NOT functions, however, since each input is related to more than one output.
    • Horizontal lines ARE functions because the relation (set of points) has the characteristic that each input is related to exactly one output.
  • Formulas and Problem-Solving

    • The formula relating gratuity (G), cost (c), and desired percent gratuity (r, expressed as a decimal).
  • Absolute Value

    • Absolute value is closely related to the mathematical and physical concepts of magnitude, distance, and norm.
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