relation

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.